Image coding method based on transform and apparatus therefor

ABSTRACT

An image decoding method according to the present document may comprise the steps of: deriving an intra prediction mode of a chroma block as a cross-component linear model (CCLM) mode on the basis of intra prediction mode information; updating the intra prediction mode of the chroma block on the basis of an intra prediction mode of a luma block corresponding to the chroma block; when the chroma block is not square, remapping the updated intra prediction mode to a wide-angle intra prediction mode; and determining an LFNST set including LFNST matrices on the basis of the remapped intra prediction mode.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.17/732,126, filed on Apr. 28, 2022, which is a continuation pursuant to35 U.S.C. § 119(e) of International Application No. PCT/KR2020/014929,with an international filing date of Oct. 29, 2020, which claims thebenefit of U.S. Provisional Patent Application No. 62/927,662, filed onOct. 29, 2019, the contents of which are hereby incorporated byreference herein in their entirety.

TECHNICAL FIELD

The present disclosure relates generally to an image coding technologyand, more particularly, to an image coding method based on a transformin an image coding system and an apparatus therefor.

RELATED ART

Nowadays, the demand for high-resolution and high-quality images/videossuch as 4K, 8K or more ultra high definition (UHD) images/videos hasbeen increasing in various fields. As the image/video data becomeshigher resolution and higher quality, the transmitted information amountor bit amount increases as compared to the conventional image data.Therefore, when image data is transmitted using a medium such as aconventional wired/wireless broadband line or image/video data is storedusing an existing storage medium. the transmission cost and the storagecost thereof are increased.

Further, nowadays, the interest and demand for immersive media such asvirtual reality (VR), artificial reality (AR) content or hologram, orthe like is increasing, and broadcasting for images/videos having imagefeatures different from those of real images, such as a game image isincreasing.

Accordingly, there is a need for a highly efficient image/videocompression technique for effectively compressing and transmitting orstoring, and reproducing information of high resolution and high qualityimages/videos having various features as described above.

SUMMARY

A technical aspect of the present disclosure is to provide a method andan apparatus for increasing image coding efficiency.

Another technical aspect of the present disclosure is to provide amethod and an apparatus for increasing efficiency in coding an LFNSTindex.

Still another technical aspect of the present disclosure is to provide amethod and an apparatus for increasing efficiency of a second transformthrough coding of an LFNST index.

Yet another technical aspect of the present disclosure is to provide animage coding method and an image coding apparatus for deriving an LFNSTtransform set using an intra mode for a luma block in a CCLM mode.

According to an embodiment of the present disclosure, there is providedan image decoding method performed by a decoding apparatus. The methodincludes deriving an intra prediction mode for a chroma block as across-component linear model (CCLM) mode based on the intra predictionmode information; updating the intra prediction mode for the chromablock based on an intra prediction mode for a luma block correspondingto the chroma block; remapping the updated intra prediction mode to awide-angle intra prediction mode when the chroma block is not a square;determining an LFNST set comprising LFNST matrices based on the remappedintra prediction mode; deriving transform coefficients for the chromablock based on an LFNST matrix derived from the LFNST index and theLFNST set; and deriving residual samples for the chroma block based onthe transform coefficients.

The updated intra prediction mode is derived as an intra prediction modecorresponding to a specific position in the luma block, and the specificposition is set based on a color format of the chroma block.

The specific position is set to ((xTbY+(nTbW*SubWidthC)/2),(yTbY+(nTbH*SubHeightC)/2)), xTbY and yTbY denote top-left coordinatesof the luma block, nTbW and nTbH denote a width and a height of thechroma block, and SubWidthC and SubHeightC denote variablescorresponding to the color format.

When the color formal is 4:2:0, SubWidthC and SubHeightC are 2, and whenthe color format is 4:2:2. SubWidthC is 2 and SubHeightC is 1.

When the intra prediction mode corresponding to the specific position isa palette mode or an IBC mode, the intra prediction mode of the chromablock is updated to an intra DC mode.

When the intra prediction mode corresponding to the specific position isan MIP mode, the intra prediction mode of the chroma block is updated toan intra planar mode.

When the width of the chroma block is greater than the height, theupdated intra mode is 2 or more and the updated intra mode is less thanvariable (whRatio >1)?(8+2*whRatio):8 [where whRatio is Abs(Log2(nW/nH))], the updated intra mode is remapped to “updated intramode+65”.

When the height of the chroma block is greater than the width, theupdated intra mode is 66 or less, and the updated intra mode is greaterthan variable (whRatio >1)?(60−2*whRatio):60 [where whRatio is Abs(Log2(nW/nH))], the updated intra mode is remapped to “updated intramode−67”.

According to another embodiment of the present disclosure, there isprovided an image encoding method performed by an encoding apparatus.The method includes deriving an intra prediction mode for a chroma blockas a cross-component linear model (CCLM) mode; deriving predictionsamples for the chroma block based on the CCLM mode; deriving residualsamples for the chroma block based on the prediction samples; updatingthe intra prediction mode for the chroma block based on an intraprediction mode for a luma block corresponding to the chroma block;remapping the updated intra prediction mode to a wide-angle intraprediction mode when the chroma block is not a square; determining anLFNST set comprising LFNST matrices based on the remapped intraprediction mode; and deriving modified transform coefficients for thechroma block based on the residual samples and the LFNST matrix.

According to still another embodiment of the present disclosure, theremay be provided a digital storage medium that stores image dataincluding encoded image information and a bitstream generated accordingto an image encoding method performed by an encoding apparatus.

According to yet another embodiment of the present disclosure, there maybe provided a digital storage medium that stores image data includingencoded image information and a bitstream to cause a decoding apparatusto perform the image decoding method.

According to the present disclosure, it is possible to increase overallimage/video compression efficiency.

According to the present disclosure, it is possible to increaseefficiency in coding an LFNST index.

According to the present disclosure, it is possible to increaseefficiency of a second transform through coding of an LFNST index.

According to the present disclosure, it is possible to provide an imagecoding method and an image coding apparatus for deriving an LFNSTtransform set using an intra mode for a luma block in a CCLM mode.

The effects that can be obtained through specific examples of thepresent disclosure are not limited to the effects listed above. Forexample, there may be various technical effects that a person havingordinary skill in the related art can understand or derive from thepresent disclosure. Accordingly, specific effects of the presentdisclosure are not limited to those explicitly described in the presentdisclosure and may include various effects that can be understood orderived from the technical features of the present disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically illustrates an example of a video/image codingsystem to which the present disclosure is applicable.

FIG. 2 is a diagram schematically illustrating a configuration of avideo/image encoding apparatus to which the present disclosure isapplicable.

FIG. 3 is a diagram schematically illustrating a configuration of avideo/image decoding apparatus to which the present disclosure isapplicable.

FIG. 4 illustrates the structure of a content streaming system to whichthe present disclosure is applied.

FIG. 5 schematically illustrates a multiple transform techniqueaccording to an embodiment of the present disclosure.

FIG. 6 exemplarily shows intra directional modes of 65 predictiondirections.

FIG. 7 is a diagram for explaining RST according to an embodiment of thepresent.

FIG. 8 is a diagram illustrating a sequence of arranging output data ofa forward primary transformation into a one-dimensional vector accordingto an example.

FIG. 9 is a diagram illustrating a sequence of arranging output data ofa forward secondary transform into a two-dimensional block according toan example.

FIG. 10 is a diagram illustrating wide-angle intra prediction modesaccording to an embodiment of the present document.

FIG. 11 is a diagram illustrating a block shape to which the LFNST isapplied.

FIG. 12 is a diagram illustrating an arrangement of output data of aforward LFNST according to an example.

FIG. 13 illustrates zeroing-out in a block to which a 4×4 LFNST isapplied according to an example.

FIG. 14 illustrates zeroing-out in a block to which an 8×8 LFNST isapplied according to an example.

FIG. 15 illustrates a CCLM applicable when deriving an intra predictionmode for a chroma block according to an embodiment.

FIG. 16 is a flowchart illustrating the operation of a video decodingapparatus according to an embodiment of the present disclosure.

FIG. 17 is a flowchart illustrating the operation of a video encodingapparatus according to an embodiment of the present disclosure.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

While the present disclosure may be susceptible to various modificationsand include various embodiments, specific embodiments thereof have beenshown in the drawings by way of example and will now be described indetail. However, this is not intended to limit the present disclosure tothe specific embodiments disclosed herein. The terminology used hereinis for the purpose of describing specific embodiments only, and is notintended to limit technical idea of the present disclosure. The singularforms may include the plural forms unless the context clearly indicatesotherwise. The terms such as “include” and “have” are intended toindicate that features, numbers, steps, operations, elements,components, or combinations thereof used in the following descriptionexist, and thus should not be understood as that the possibility ofexistence or addition of one or more different features, numbers, steps,operations, elements, components, or combinations thereof is excluded inadvance.

Meanwhile, each component on the drawings described herein isillustrated independently for convenience of description as tocharacteristic functions different from each other, and however, it isnot meant that each component is realized by a separate hardware orsoftware. For example, any two or more of these components may becombined to form a single component, and any single component may bedivided into plural components. The embodiments in which components arecombined and/or divided will belong to the scope of the patent right ofthe present disclosure as long as they do not depart from the essence ofthe present disclosure.

Hereinafter, preferred embodiments of the present disclosure will beexplained in more detail while referring to the attached drawings. Inaddition, the same reference signs are used for the same components onthe drawings, and repeated descriptions for the same components will beomitted.

This document relates to video/image coding. For example, themethod/example disclosed in this document may relate to a VVC (VersatileVideo Coding) standard (ITU-T Rec. H.266), a next-generation video/imagecoding standard after VVC, or other video coding related standards(e.g., HEVC (High Efficiency Video Coding) standard (ITU-T Rec. H.265),EVC (essential video coding) standard, AVS2 standard, etc.).

In this document, a variety of embodiments relating to video/imagecoding may be provided, and, unless specified to the contrary, theembodiments may be combined to each other and be performed.

In this document, a video may mean a set of a series of images overtime. Generally a picture means a unit representing an image at aspecific time zone, and a slice/tile is a unit constituting a part ofthe picture. The slice/tile may include one or more coding tree units(CTUs). One picture may be constituted by one or more slices/tiles. Onepicture may be constituted by one or more tile groups. One tile groupmay include one or more tiles.

A pixel or a pel may mean a smallest unit constituting one picture (orimage). Also, ‘sample’ may be used as a term corresponding to a pixel. Asample may generally represent a pixel or a value of a pixel, and mayrepresent only a pixel/pixel value of a luma component or only apixel/pixel value of a chroma component. Alternatively, the sample mayrefer to a pixel value in the spatial domain, or when this pixel valueis converted to the frequency domain, it may refer to a transformcoefficient in the frequency domain.

A unit may represent the basic unit of image processing. The unit mayinclude at least one of a specific region and information related to theregion. One unit may include one luma block and two chroma (e.g., cb,cr) blocks. The unit and a term such as a block, an area, or the likemay be used in place of each other according to circumstances. In ageneral case, an M N block may include a set (or an array) of samples(or sample arrays) or transform coefficients consisting of M columns andN rows.

In this document, the term “/” and “,” should be interpreted to indicate“and/or.” For instance, the expression “A/B” may mean “A and/or B.”Further, “A, B” may mean “A and/or B.” Further, “A/B/C” may mean “atleast one of A, B, and/or C.” Also, “A/B/C” may mean “at least one of A,B. and/or C.”

Further, in the document, the term “or” should be interpreted toindicate “and/or.” For instance, the expression “A or B” may include 1)only A, 2) only B. and/or 3) both A and B. In other words, the term “or”in this document should be interpreted to indicate “additionally oralternatively.”

In the present disclosure, “at least one of A and B” may mean “only A”,“only B”, or “both A and B”. In addition, in the present disclosure, theexpression “at least one of A or B” or “at least one of A and/or B” maybe interpreted as “at least one of A and B”.

In addition, in the present disclosure, “at least one of A, B. and C”may mean “only A”, “only B”, “only C”, or “any combination of A, B, andC”. In addition, “at least one of A, B, or C” or “at least one of A, B,and/or C” may mean “at least one of A, B, and C”.

In addition, a parenthesis used in the present disclosure may mean “forexample”. Specifically, when indicated as “prediction (intraprediction)”, it may mean that “intra prediction” is proposed as anexample of “prediction”. That is, “prediction” in the present disclosureis not limited to “intra prediction”, and “intra prediction” may beproposed as an example of “prediction”. In addition, when indicated as“prediction (i.e., intra prediction)”, it may also mean that “intraprediction” is proposed as an example of “prediction”.

Technical features individually described in one figure in the presentdisclosure may be individually implemented or may be simultaneouslyimplemented.

FIG. 1 schematically illustrates an example of a video/image codingsystem to which the present disclosure is applicable.

Referring to FIG. 1 , the video/image coding system may include a firstdevice (source device) and a second device (receive device). The sourcedevice may deliver encoded video/image information or data in the formof a file or streaming to the receive device via a digital storagemedium or network.

The source device may include a video source, an encoding apparatus, anda transmitter. The receive device may include a receiver, a decodingapparatus, and a renderer. The encoding apparatus may be called avideo/image encoding apparatus, and the decoding apparatus may be calleda video/image decoding apparatus. The transmitter may be included in theencoding apparatus. The receiver may be included in the decodingapparatus. The renderer may include a display, and the display may beconfigured as a separate device or an external component.

The video source may obtain a video/image through a process ofcapturing, synthesizing, or generating a video/image. The video sourcemay include a video/image capture device and/or a video/image generatingdevice. The video/image capture device may include, for example, one ormore cameras, video/image archives including previously capturedvideo/images, or the like. The video/image generating device mayinclude, for example, a computer, a tablet and a smartphone, and may(electronically) generate a video/image. For example, a virtualvideo/image may be generated through a computer or the like. In thiscase, the video/image capturing process may be replaced by a process ofgenerating related data.

The encoding apparatus may encode an input video/image. The encodingapparatus may perform a series of procedures such as prediction,transform, and quantization for compression and coding efficiency. Theencoded data (encoded video/image information) may be output in the formof a bitstream.

The transmitter may transmit the encoded video/image information or dataoutput in the form of a bitstream to the receiver of the receive devicethrough a digital storage medium or a network in the form of a file orstreaming. The digital storage medium may include various storagemediums such as USB, SD, CD, DVD, Blu-ray, HDD, SSD, and the like. Thetransmitter may include an element for generating a media file through apredetermined file format, and may include an element for transmissionthrough a broadcast/communication network. The receiver mayreceive/extract the bitstream and transmit the received/extractedbitstream to the decoding apparatus.

The decoding apparatus may decode a video/image by performing a seriesof procedures such as dequantization, inverse transform, prediction, andthe like corresponding to the operation of the encoding apparatus.

The renderer may render the decoded video/image. The renderedvideo/image may be displayed through the display.

FIG. 2 is a diagram schematically illustrating a configuration of avideo/image encoding apparatus to which the present disclosure isapplicable. Hereinafter, what is referred to as the video encodingapparatus may include an image encoding apparatus.

Referring to FIG. 2 , the encoding apparatus 200 may include an imagepartitioner 210, a predictor 220, a residual processor 230, an entropyencoder 240, an adder 250, a filter 260, and a memory 270. The predictor220 may include an inter predictor 221 and an intra predictor 222. Theresidual processor 230 may include a transformer 232, a quantizer 233, adequantizer 234, an inverse transformer 235. The residual processor 230may further include a subtractor 231. The adder 250 may be called areconstructor or reconstructed block generator. The image partitioner210, the predictor 220, the residual processor 230, the entropy encoder240, the adder 250, and the filter 260, which have been described above,may be constituted by one or more hardware components (e.g., encoderchipsets or processors) according to an embodiment. Further, the memory270 may include a decoded picture buffer (DPB), and may be constitutedby a digital storage medium. The hardware component may further includethe memory 270 as an internal/external component.

The image partitioner 210 may partition an input image (or a picture ora frame) input to the encoding apparatus 200 into one or more processingunits. As one example, the processing unit may be called a coding unit(CU). In this case, starting with a coding tree unit (CTU) or thelargest coding unit (LCU), the coding unit may be recursivelypartitioned according to the Quad-tree binary-tree ternary-tree (QTBTT)structure. For example, one coding unit may be divided into a pluralityof coding units of a deeper depth based on the quad-tree structure, thebinary-tree structure, and/or the ternary structure. In this case, forexample, the quad-tree structure may be applied first and thebinary-tree structure and/or the ternary structure may be applied later.Alternatively, the binary-tree structure may be applied first. Thecoding procedure according to the present disclosure may be performedbased on the final coding unit which is not further partitioned. In thiscase, the maximum coding unit may be used directly as a final codingunit based on coding efficiency according to the image characteristic.Alternatively, the coding unit may be recursively partitioned intocoding units of a further deeper depth as needed, so that the codingunit of an optimal size may be used as a final coding unit. Here, thecoding procedure may include procedures such as prediction, transform,and reconstruction, which will be described later. As another example,the processing unit may further include a prediction unit (PU) or atransform unit (TU). In this case, the prediction unit and the transformunit may be split or partitioned from the above-described final codingunit. The prediction unit may be a unit of sample prediction, and thetransform unit may be a unit for deriving a transform coefficient and/ora unit for deriving a residual signal from a transform coefficient.

The unit and a term such as a block, an area, or the like may be used inplace of each other according to circumstances. In a general case, anM×N block may represent a set of samples or transform coefficientsconsisting of M columns and N rows. The sample may generally represent apixel or a value of a pixel, and may represent only a pixel/pixel valueof a luma component, or only a pixel/pixel value of a chroma component.The sample may be used as a term corresponding to a pixel or a pel ofone picture (or image).

The subtractor 231 subtracts a prediction signal (predicted block,prediction sample array) output from the inter predictor 221 or theintra predictor 222 from an input image signal (original block, originalsample array) to generate a residual signal (residual block, residualsample array), and the generated residual signal is transmitted to thetransformer 232. In this case, as shown, a unit which subtracts theprediction signal (predicted block, prediction sample array) from theinput image signal (original block, original sample array) in theencoder 200 may be called the subtractor 231. The predictor may performprediction on a processing target block (hereinafter, referred to as‘current block’), and may generate a predicted block includingprediction samples for the current block. The predictor may determinewhether intra prediction or inter prediction is applied on a currentblock or CU basis. As discussed later in the description of eachprediction mode, the predictor may generate various information relatingto prediction, such as prediction mode information, and transmit thegenerated information to the entropy encoder 240. The information on theprediction may be encoded in the entropy encoder 240 and output in theform of a bitstream.

The intra predictor 222 may predict the current block by referring tosamples in the current picture. The referred samples may be located inthe neighbor of or apart from the current block according to theprediction mode. In the intra prediction, prediction modes may include aplurality of non-directional modes and a plurality of directional modes.The non-directional modes may include, for example, a DC mode and aplanar mode. The directional mode may include, for example, 33directional prediction modes or 65 directional prediction modesaccording to the degree of detail of the prediction direction. However,this is merely an example, and more or less directional prediction modesmay be used depending on a setting. The intra predictor 222 maydetermine the prediction mode applied to the current block by using theprediction mode applied to the neighboring block.

The inter predictor 221 may derive a predicted block for the currentblock based on a reference block (reference sample array) specified by amotion vector on a reference picture. At this time, in order to reducethe amount of motion information transmitted in the inter predictionmode, the motion information may be predicted on a block, subblock, orsample basis based on correlation of motion information between theneighboring block and the current block. The motion information mayinclude a motion vector and a reference picture index. The motioninformation may further include inter prediction direction (L0prediction, L1 prediction, Bi prediction, etc.) information. In the caseof inter prediction, the neighboring block may include a spatialneighboring block existing in the current picture and a temporalneighboring block existing in the reference picture. The referencepicture including the reference block and the reference pictureincluding the temporal neighboring block may be same to each other ordifferent from each other. The temporal neighboring block may be calleda collocated reference block, a collocated CU (colCU), and the like, andthe reference picture including the temporal neighboring block may becalled a collocated picture (colPic). For example, the inter predictor221 may configure a motion information candidate list based onneighboring blocks and generate information indicating which candidateis used to derive a motion vector and/or a reference picture index ofthe current block. Inter prediction may be performed based on variousprediction modes. For example, in the case of a skip mode and a mergemode, the inter predictor 221 may use motion information of theneighboring block as motion information of the current block. In theskip mode, unlike the merge mode, the residual signal may not betransmitted. In the case of the motion information prediction (motionvector prediction, MVP) mode, the motion vector of the neighboring blockmay be used as a motion vector predictor and the motion vector of thecurrent block may be indicated by signaling a motion vector difference.

The predictor 220 may generate a prediction signal based on variousprediction methods. For example, the predictor may apply intraprediction or inter prediction for prediction on one block, and, aswell, may apply intra prediction and inter prediction at the same time.This may be called combined inter and intra prediction (CIIP). Further,the predictor may be based on an intra block copy (IBC) prediction mode,or a palette mode in order to perform prediction on a block. The IBCprediction mode or palette mode may be used for content image/videocoding of a game or the like, such as screen content coding (SCC).Although the IBC basically performs prediction in a current block, itcan be performed similarly to inter prediction in that it derives areference block in a current block. That is, the IBC may use at leastone of inter prediction techniques described in the present disclosure.

The prediction signal generated through the inter predictor 221 and/orthe intra predictor 222 may be used to generate a reconstructed signalor to generate a residual signal. The transformer 232 may generatetransform coefficients by applying a transform technique to the residualsignal. For example, the transform technique may include at least one ofa discrete cosine transform (DCT), a discrete sine transform (DST), aKarhunen-Loève transform (KLT), a graph-based transform (GBT), or aconditionally non-linear transform (CNT). Here, the GBT means transformobtained from a graph when relationship information between pixels isrepresented by the graph. The CNT refers to transform obtained based ona prediction signal generated using all previously reconstructed pixels.In addition, the transform process may be applied to square pixel blockshaving the same size or may be applied to blocks having a variable sizerather than the square one.

The quantizer 233 may quantize the transform coefficients and transmitthem to the entropy encoder 240, and the entropy encoder 240 may encodethe quantized signal (information on the quantized transformcoefficients) and output the encoded signal in a bitstream. Theinformation on the quantized transform coefficients may be referred toas residual information. The quantizer 233 may rearrange block typequantized transform coefficients into a one-dimensional vector formbased on a coefficient scan order, and generate information on thequantized transform coefficients based on the quantized transformcoefficients of the one-dimensional vector form. The entropy encoder 240may perform various encoding methods such as, for example, exponentialGolomb, context-adaptive variable length coding (CAVLC),context-adaptive binary arithmetic coding (CABAC), and the like. Theentropy encoder 240 may encode information necessary for video/imagereconstruction other than quantized transform coefficients (e.g. valuesof syntax elements, etc.) together or separately. Encoded information(e.g., encoded video/image information) may be transmitted or stored ona unit basis of a network abstraction layer (NAL) in the form of abitstream. The video/image information may further include informationon various parameter sets such as an adaptation parameter set (APS), apicture parameter set (PPS), a sequence parameter set (SPS), a videoparameter set (VPS) or the like. Further, the video/image informationmay further include general constraint information. In the presentdisclosure, information and/or syntax elements which aretransmitted/signaled to the decoding apparatus from the encodingapparatus may be included in video/image information. The video/imageinformation may be encoded through the above-described encodingprocedure and included in the bitstream. The bitstream may betransmitted through a network, or stored in a digital storage medium.Here, the network may include a broadcast network, a communicationnetwork and/or the like, and the digital storage medium may includevarious storage media such as USB, SD, CD, DVD, Blu-ray, HDD, SSD, andthe like. A transmitter (not shown) which transmits a signal output fromthe entropy encoder 240 and/or a storage (not shown) which stores it maybe configured as an internal/external element of the encoding apparatus200, or the transmitter may be included in the entropy encoder 240.

Quantized transform coefficients output from the quantizer 233 may beused to generate a prediction signal. For example, by applyingdequantization and inverse transform to quantized transform coefficientsthrough the dequantizer 234 and the inverse transformer 235, theresidual signal (residual block or residual samples) may bereconstructed. The adder 155 adds the reconstructed residual signal to aprediction signal output from the inter predictor 221 or the intrapredictor 222, so that a reconstructed signal (reconstructed picture,reconstructed block, reconstructed sample array) may be generated. Whenthere is no residual for a processing target block as in a case wherethe skip mode is applied, the predicted block may be used as areconstructed block. The adder 250 may be called a reconstructor or areconstructed block generator. The generated reconstructed signal may beused for intra prediction of a next processing target block in thecurrent block, and as described later, may be used for inter predictionof a next picture through filtering.

Meanwhile, in the picture encoding and/or reconstructing process, lumamapping with chroma scaling (LMCS) may be applied.

The filter 260 may improve subjective/objective video quality byapplying the filtering to the reconstructed signal. For example, thefilter 260 may generate a modified reconstructed picture by applyingvarious filtering methods to the reconstructed picture, and may storethe modified reconstructed picture in the memory 270, specifically inthe DPB of the memory 270. The various filtering methods may include,for example, deblocking filtering, sample adaptive offset, an adaptiveloop filter, a bilateral filter or the like. As discussed later in thedescription of each filtering method, the filter 260 may generatevarious information relating to filtering, and transmit the generatedinformation to the entropy encoder 240. The information on the filteringmay be encoded in the entropy encoder 240 and output in the form of abitstream.

The modified reconstructed picture which has been transmitted to thememory 270 may be used as a reference picture in the inter predictor221. Through this, the encoding apparatus can avoid prediction mismatchin the encoding apparatus 100 and a decoding apparatus when the interprediction is applied, and can also improve coding efficiency.

The memory 270 DPB may store the modified reconstructed picture in orderto use it as a reference picture in the inter predictor 221. The memory270 may store motion information of a block in the current picture, fromwhich motion information has been derived (or encoded) and/or motioninformation of blocks in an already reconstructed picture. The storedmotion information may be transmitted to the inter predictor 221 to beutilized as motion information of a neighboring block or motioninformation of a temporal neighboring block. The memory 270 may storereconstructed samples of reconstructed blocks in the current picture,and transmit them to the intra predictor 222.

FIG. 3 is a diagram schematically illustrating a configuration of avideo/image decoding apparatus to which the present disclosure isapplicable.

Referring to FIG. 3 , the video decoding apparatus 300 may include anentropy decoder 310, a residual processor 320, a predictor 330, an adder340, a filter 350 and a memory 360. The predictor 330 may include aninter predictor 331 and an intra predictor 332. The residual processor320 may include a dequantizer 321 and an inverse transformer 321. Theentropy decoder 310, the residual processor 320, the predictor 330, theadder 340, and the filter 350, which have been described above, may beconstituted by one or more hardware components (e.g., decoder chipsetsor processors) according to an embodiment. Further, the memory 360 mayinclude a decoded picture buffer (DPB), and may be constituted by adigital storage medium. The hardware component may further include thememory 360 as an internal/external component.

When a bitstream including video/image information is input, thedecoding apparatus 300 may reconstruct an image correspondingly to aprocess by which video/image information has been processed in theencoding apparatus of FIG. 2 . For example, the decoding apparatus 300may derive units/blocks based on information relating to block partitionobtained from the bitstream. The decoding apparatus 300 may performdecoding by using a processing unit applied in the encoding apparatus.Therefore, the processing unit of decoding may be, for example, a codingunit, which may be partitioned along the quad-tree structure, thebinary-tree structure, and/or the ternary-tree structure from a codingtree unit or a largest coding unit. One or more transform units may bederived from the coding unit. And, the reconstructed image signaldecoded and output through the decoding apparatus 300 may be reproducedthrough a reproducer.

The decoding apparatus 300 may receive a signal output from the encodingapparatus of FIG. 2 in the form of a bitstream, and the received signalmay be decoded through the entropy decoder 310. For example, the entropydecoder 310 may parse the bitstream to derive information (e.g.,video/image information) required for image reconstruction (or picturereconstruction). The video/image information may further includeinformation on various parameter sets such as an adaptation parameterset (APS), a picture parameter set (PPS), a sequence parameter set(SPS), a video parameter set (VPS) or the like. Further, the video/imageinformation may further include general constraint information. Thedecoding apparatus may decode a picture further based on information onthe parameter set and/or the general constraint information. In thepresent disclosure, signaled/received information and/or syntaxelements, which will be described later, may be decoded through thedecoding procedure and be obtained from the bitstream. For example, theentropy decoder 310 may decode information in the bitstream based on acoding method such as exponential Golomb encoding, CAVLC, CABAC, or thelike, and may output a value of a syntax element necessary for imagereconstruction and quantized values of a transform coefficient regardinga residual. More specifically, a CABAC entropy decoding method mayreceive a bin corresponding to each syntax element in a bitstream,determine a context model using decoding target syntax elementinformation and decoding information of neighboring and decoding targetblocks, or information of symbol/bin decoded in a previous step, predictbin generation probability according to the determined context model andperform arithmetic decoding of the bin to generate a symbolcorresponding to each syntax element value. Here, the CABAC entropydecoding method may update the context model using information of asymbol/bin decoded for a context model of the next symbol/bin afterdetermination of the context model. Information on prediction amonginformation decoded in the entropy decoder 310 may be provided to thepredictor (inter predictor 332 and intra predictor 331), and residualvalues, that is, quantized transform coefficients, on which entropydecoding has been performed in the entropy decoder 310, and associatedparameter information may be input to the residual processor 320. Theresidual processor 320 may derive a residual signal (residual block,residual samples, residual sample array). Further, information onfiltering among information decoded in the entropy decoder 310 may beprovided to the filter 350. Meanwhile, a receiver (not shown) whichreceives a signal output from the encoding apparatus may furtherconstitute the decoding apparatus 300 as an internal/external element,and the receiver may be a component of the entropy decoder 310.Meanwhile, the decoding apparatus according to the present disclosuremay be called a video/image/picture coding apparatus, and the decodingapparatus may be classified into an information decoder(video/image/picture information decoder) and a sample decoder(video/image/picture sample decoder). The information decoder mayinclude the entropy decoder 310, and the sample decoder may include atleast one of the dequantizer 321, the inverse transformer 322, the adder340, the filter 350, the memory 360, the inter predictor 332, and theintra predictor 331.

The dequantizer 321 may output transform coefficients by dequantizingthe quantized transform coefficients. The dequantizer 321 may rearrangethe quantized transform coefficients in the form of a two-dimensionalblock. In this case, the rearrangement may perform rearrangement basedon an order of coefficient scanning which has been performed in theencoding apparatus. The dequantizer 321 may perform dequantization onthe quantized transform coefficients using quantization parameter (e.g.,quantization step size information), and obtain transform coefficients.

The dequantizer 322 obtains a residual signal (residual block, residualsample array) by inverse transforming transform coefficients.

The predictor may perform prediction on the current block, and generatea predicted block including prediction samples for the current block.The predictor may determine whether intra prediction or inter predictionis applied to the current block based on the information on predictionoutput from the entropy decoder 310, and specifically may determine anintra/inter prediction mode.

The predictor may generate a prediction signal based on variousprediction methods. For example, the predictor may apply intraprediction or inter prediction for prediction on one block, and, aswell, may apply intra prediction and inter prediction at the same time.This may be called combined inter and intra prediction (CIIP). Inaddition, the predictor may perform intra block copy (IBC) forprediction on a block. The intra block copy may be used for contentimage/video coding of a game or the like, such as screen content coding(SCC). Although the IBC basically performs prediction in a currentblock, it can be performed similarly to inter prediction in that itderives a reference block in a current block. That is, the IBC may useat least one of inter prediction techniques described in the presentdisclosure.

The intra predictor 331 may predict the current block by referring tothe samples in the current picture. The referred samples may be locatedin the neighbor of or apart from the current block according to theprediction mode. In the intra prediction, prediction modes may include aplurality of non-directional modes and a plurality of directional modes.The intra predictor 331 may determine the prediction mode applied to thecurrent block by using the prediction mode applied to the neighboringblock.

The inter predictor 332 may derive a predicted block for the currentblock based on a reference block (reference sample array) specified by amotion vector on a reference picture. At this time, in order to reducethe amount of motion information transmitted in the inter predictionmode, the motion information may be predicted on a block, subblock, orsample basis based on correlation of motion information between theneighboring block and the current block. The motion information mayinclude a motion vector and a reference picture index. The motioninformation may further include inter prediction direction (L0prediction, L1 prediction, Bi prediction, etc.) information. In the caseof inter prediction, the neighboring block may include a spatialneighboring block existing in the current picture and a temporalneighboring block existing in the reference picture. For example, theinter predictor 332 may configure a motion information candidate listbased on neighboring blocks, and derive a motion vector and/or areference picture index of the current block based on received candidateselection information. Inter prediction may be performed based onvarious prediction modes, and the information on prediction may includeinformation indicating a mode of inter prediction for the current block.

The adder 340 may generate a reconstructed signal (reconstructedpicture, reconstructed block, reconstructed sample array) by adding theobtained residual signal to the prediction signal (predicted block,prediction sample array) output from the predictor 330. When there is noresidual for a processing target block as in a case where the skip modeis applied, the predicted block may be used as a reconstructed block.

The adder 340 may be called a reconstructor or a reconstructed blockgenerator. The generated reconstructed signal may be used for intraprediction of a next processing target block in the current block, andas described later, may be output through filtering or be used for interprediction of a next picture.

Meanwhile, in the picture decoding process, luma mapping with chromascaling (LMCS) may be applied.

The filter 350 may improve subjective/objective video quality byapplying the filtering to the reconstructed signal. For example, thefilter 350 may generate a modified reconstructed picture by applyingvarious filtering methods to the reconstructed picture, and may transmitthe modified reconstructed picture in the memory 360, specifically inthe DPB of the memory 360. The various filtering methods may include,for example, deblocking filtering, sample adaptive offset, an adaptiveloop filter, a bilateral filter or the like.

The (modified)reconstructed picture which has been stored in the DPB ofthe memory 360 may be used as a reference picture in the inter predictor332. The memory 360 may store motion information of a block in thecurrent picture, from which motion information has been derived (ordecoded) and/or motion information of blocks in an already reconstructedpicture. The stored motion information may be transmitted to the interpredictor 260 to be utilized as motion information of a neighboringblock or motion information of a temporal neighboring block. The memory360 may store reconstructed samples of reconstructed blocks in thecurrent picture, and transmit them to the intra predictor 331.

In this specification, the examples described in the predictor 330, thedequantizer 321, the inverse transformer 322, and the filter 350 of thedecoding apparatus 300 may be similarly or correspondingly applied tothe predictor 220, the dequantizer 234, the inverse transformer 235, andthe filter 260 of the encoding apparatus 200, respectively.

As described above, prediction is performed in order to increasecompression efficiency in performing video coding. Through this, apredicted block including prediction samples for a current block, whichis a coding target block, may be generated. Here, the predicted blockincludes prediction samples in a space domain (or pixel domain). Thepredicted block may be identically derived in the encoding apparatus andthe decoding apparatus, and the encoding apparatus may increase imagecoding efficiency by signaling to the decoding apparatus not originalsample value of an original block itself but information on residual(residual information) between the original block and the predictedblock. The decoding apparatus may derive a residual block includingresidual samples based on the residual information, generate areconstructed block including reconstructed samples by adding theresidual block to the predicted block, and generate a reconstructedpicture including reconstructed blocks.

The residual information may be generated through transform andquantization procedures. For example, the encoding apparatus may derivea residual block between the original block and the predicted block,derive transform coefficients by performing a transform procedure onresidual samples (residual sample array) included in the residual block,and derive quantized transform coefficients by performing a quantizationprocedure on the transform coefficients, so that it may signalassociated residual information to the decoding apparatus (through abitstream). Here, the residual information may include valueinformation, position information, a transform technique, transformkernel, a quantization parameter or the like of the quantized transformcoefficients. The decoding apparatus may perform aquantization/dequantization procedure and derive the residual samples(or residual sample block), based on residual information. The decodingapparatus may generate a reconstructed block based on a predicted blockand the residual block. The encoding apparatus may derive a residualblock by dequantizing/inverse transforming quantized transformcoefficients for reference for inter prediction of a next picture, andmay generate a reconstructed picture based on this.

FIG. 4 illustrates the structure of a content streaming system to whichthe present disclosure is applied.

Further, the contents streaming system to which the present disclosureis applied may largely include an encoding server, a streaming server, aweb server, a media storage, a user equipment, and a multimedia inputdevice.

The encoding server functions to compress to digital data the contentsinput from the multimedia input devices, such as the smart phone, thecamera, the camcoder and the like, to generate a bitstream, and totransmit it to the streaming server. As another example, in a case wherethe multimedia input device, such as, the smart phone, the camera, thecamcoder or the like, directly generates a bitstream, the encodingserver may be omitted. The bitstream may be generated by an encodingmethod or a bitstream generation method to which the present disclosureis applied. And the streaming server may store the bitstream temporarilyduring a process to transmit or receive the bitstream.

The streaming server transmits multimedia data to the user equipment onthe basis of a user's request through the web server, which functions asan instrument that informs a user of what service there is. When theuser requests a service which the user wants, the web server transfersthe request to the streaming server, and the streaming server transmitsmultimedia data to the user. In this regard, the contents streamingsystem may include a separate control server, and in this case, thecontrol server functions to control commands/responses betweenrespective equipments in the content streaming system.

The streaming server may receive contents from the media storage and/orthe encoding server. For example, in a case the contents are receivedfrom the encoding server, the contents may be received in real time. Inthis case, the streaming server may store the bitstream for apredetermined period of time to provide the streaming service smoothly.

For example, the user equipment may include a mobile phone, a smartphone, a laptop computer, a digital broadcasting terminal, a personaldigital assistant (PDA), a portable multimedia player (PMP), anavigation, a slate PC, a tablet PC, an ultrabook, a wearable device(e.g., a watch-type terminal (smart watch), a glass-type terminal (smartglass), a head mounted display (HMD)), a digital TV, a desktop computer,a digital signage or the like. Each of servers in the contents streamingsystem may be operated as a distributed server, and in this case, datareceived by each server may be processed in distributed manner.

FIG. 5 schematically illustrates a multiple transform techniqueaccording to an embodiment of the present disclosure.

Referring to FIG. 5 , a transformer may correspond to the transformer inthe foregoing encoding apparatus of FIG. 2 , and an inverse transformermay correspond to the inverse transformer in the foregoing encodingapparatus of FIG. 2 , or to the inverse transformer in the decodingapparatus of FIG. 3 .

The transformer may derive (primary) transform coefficients byperforming a primary transform based on residual samples (residualsample array) in a residual block (S510). This primary transform may bereferred to as a core transform. Herein, the primary transform may bebased on multiple transform selection (MTS), and when a multipletransform is applied as the primary transform, it may be referred to asa multiple core transform.

The multiple core transform may represent a method of transformingadditionally using discrete cosine transform (DCT) type 2 and discretesine transform (DST) type 7, DCT type 8, and/or DST type 1. That is, themultiple core transform may represent a transform method of transforminga residual signal (or residual block) of a space domain into transformcoefficients (or primary transform coefficients) of a frequency domainbased on a plurality of transform kernels selected from among the DCTtype 2, the DST type 7, the DCT type 8 and the DST type 1. Herein, theprimary transform coefficients may be called temporary transformcoefficients from the viewpoint of the transformer.

That is, when the conventional transform method is applied, transformcoefficients may be generated by applying transform from a space domainto a frequency domain to a residual signal (or residual block) based onDCT type 2. However, when the multiple core transform is applied,transform coefficients (or primary transform coefficients) may begenerated by applying transform from a space domain to a frequencydomain to a residual signal (or residual block) based on DCT type 2, DSTtype 7, DCT type 8, and/or DST type 1. Here, DCT type 2, DST type 7, DCTtype 8, and DST type 1 may be referred to as transform types, transformkernels, or transform cores. These DCT/DST types may be defined based onbasis functions.

If the multiple core transform is performed, then a vertical transformkernel and a horizontal transform kernel for a target block may beselected from among the transform kernels, a vertical transform for thetarget block may be performed based on the vertical transform kernel,and a horizontal transform for the target block may be performed basedon the horizontal transform kernel. Here, the horizontal transform mayrepresent a transform for horizontal components of the target block, andthe vertical transform may represent a transform for vertical componentsof the target block. The vertical transform kernel/horizontal transformkernel may be adaptively determined based on a prediction mode and/or atransform index of a target block (CU or sub-block) including a residualblock.

Further, according to an example, if the primary transform is performedby applying the MTS, a mapping relationship for transform kernels may beset by setting specific basis functions to predetermined values andcombining basis functions to be applied in the vertical transform or thehorizontal transform. For example, when the horizontal transform kernelis expressed as trTypeHor and the vertical direction transform kernel isexpressed as trTypeVer, a trTypeHor or trTypeVer value of 0 may be setto DCT2, a trTypeHor or trTypeVer value of 1 may be set to DST-7, and atrTypeHor or trTypeVer value of 2 may be set to DCT-8.

In this case, MTS index information may be encoded and signaled to thedecoding apparatus to indicate any one of a plurality of transformkernel sets. For example, an MTS index of 0 may indicate that bothtrTypeHor and trTypeVer values are 0, an MTS index of 1 may indicatethat both trTypeHor and trTypeVer values are 1, an MTS index of 2 mayindicate that the trTypeHor value is 2 and the trTypeVer value. Is 1, anMTS index of 3 may indicate that the trTypeHor value is 1 and thetrTypeVer value is 2, and an MTS index of 4 may indicate that both bothtrTypeHor and trTypeVer values are 2.

In one example, transform kernel sets according to MTS index informationare illustrated in the following table.

TABLE 1 tu_mts_idx[ x0 ][ y0 ] 0 1 2 3 4 trTypeHor 0 1 2 1 2 trTypeVer 01 1 2 2

The transformer may derive modified (secondary) transform coefficientsby performing the secondary transform based on the (primary) transformcoefficients (S520). The primary transform is a transform from a spatialdomain to a frequency domain, and the secondary transform refers totransforming into a more compressive expression by using a correlationexisting between (primary) transform coefficients. The secondarytransform may include a non-separable transform. In this case, thesecondary transform may be called a non-separable secondary transform(NSST), or a mode-dependent non-separable secondary transform (MDNSST).The non-separable secondary transform may represent a transform whichgenerates modified transform coefficients (or secondary transformcoefficients) for a residual signal by secondary-transforming, based ona non-separable transform matrix, (primary) transform coefficientsderived through the primary transform. At this time, the verticaltransform and the horizontal transform may not be applied separately (orhorizontal and vertical transforms may not be applied independently) tothe (primary) transform coefficients, but the transforms may be appliedat once based on the non-separable transform matrix. In other words, thenon-separable secondary transform may represent a transform method inwhich is not separately applied in the vertical direction and thehorizontal direction for the (primary) transform coefficients, and forexample, two-dimensional signals (transform coefficients) arere-arranged to a one-dimensional signal through a certain determineddirection (e.g., row-first direction or column-first direction), andthen modified transform coefficients (or secondary transformcoefficients) are generated based on the non-separable transform matrix.For example, according to a row-first order, M×N blocks are disposed ina line in an order of a first row, a second row, . . . , and an Nth row.According to a column-first order, M×N blocks are disposed in a line inan order of a first column, a second column, . . . , and an Nth column.The non-separable secondary transform may be applied to a top-leftregion of a block configured with (primary) transform coefficients(hereinafter, may be referred to as a transform coefficient block). Forexample, if the width (W) and the height (H) of the transformcoefficient block are all equal to or greater than 8, an 8×8non-separable secondary transform may be applied to a top-left 8×8region of the transform coefficient block. Further, if the width (W) andthe height (H) of the transform coefficient block are all equal to orgreater than 4, and the width (W) or the height (H) of the transformcoefficient block is less than 8, then a 4×4 non-separable secondarytransform may be applied to a top-left min(8,W)×min(8,H) region of thetransform coefficient block. However, the embodiment is not limited tothis, and for example, even if only the condition that the width (W) orheight (H) of the transform coefficient block is equal to or greaterthan 4 is satisfied, the 4×4 non-separable secondary transform may beapplied to the top-left min(8,W)×min(8,H) region of the transformcoefficient block.

Specifically, for example, if a 4×4 input block is used, thenon-separable secondary transform may be performed as follows.

The 4×4 input block X may be represented as follows.

$\begin{matrix}{X = \begin{bmatrix}X_{00} & X_{01} & X_{02} & X_{03} \\X_{10} & X_{11} & X_{12} & X_{13} \\X_{20} & X_{21} & X_{22} & X_{23} \\X_{30} & X_{31} & X_{32} & X_{33}\end{bmatrix}} & \left\lbrack {{Equation}1} \right\rbrack\end{matrix}$

If the X is represented in the form of a vector, the vector

may be represented as below.

=[X ₀₀ X ₀₁ X ₀₂ X ₀₃ X ₁₀ X ₁₁ X ₁₂ X ₁₃ X ₂₀ X ₂₁ X ₂₂ X ₂₃ X ₃₀ X ₃₁X ₃₂ X ₃₃]^(T)  [Equation 2]

In Equation 2, the vector

is a one-dimensional vector obtained by rearranging the two-dimensionalblock X of Equation 1 according to the row-first order.

In this case, the secondary non-separable transform may be calculated asbelow.

{right arrow over (F)}=T−·

  [Equation 3]

In this equation,

represents a transform coefficient vector, and T represents a 16×16(non-separable) transform matrix.

Through foregoing Equation 3, a 16×1 transform coefficient vector

may be derived, and the

may be re-organized into a 4×4 block through a scan order (horizontal,vertical, diagonal and the like). However, the above-describedcalculation is an example, and hypercube-Givens transform (HyGT) or thelike may be used for the calculation of the non-separable secondarytransform in order to reduce the computational complexity of thenon-separable secondary transform.

Meanwhile, in the non-separable secondary transform, a transform kernel(or transform core, transform type) may be selected to be modedependent. In this case, the mode may include the intra prediction modeand/or the inter prediction mode.

As described above, the non-separable secondary transform may beperformed based on an 8×8 transform or a 4×4 transform determined basedon the width (W) and the height (H) of the transform coefficient block.The 8×8 transform refers to a transform that is applicable to an 8×8region included in the transform coefficient block when both W and H areequal to or greater than 8, and the 8×8 region may be a top-left 8×8region in the transform coefficient block. Similarly, the 4×4 transformrefers to a transform that is applicable to a 4×4 region included in thetransform coefficient block when both W and H are equal to or greaterthan 4, and the 4×4 region may be a top-left 4×4 region in the transformcoefficient block. For example, an 8×8 transform kernel matrix may be a64×64/16×64 matrix, and a 4×4 transform kernel matrix may be a16×16/8×16 matrix.

Here, to select a mode-dependent transform kernel, two non-separablesecondary transform kernels per transform set for a non-separablesecondary transform may be configured for both the 8×8 transform and the4×4 transform, and there may be four transform sets. That is, fourtransform sets may be configured for the 8×8 transform, and fourtransform sets may be configured for the 4×4 transform. In this case,each of the four transform sets for the 8×8 transform may include two8×8 transform kernels, and each of the four transform sets for the 4×4transform may include two 4×4 transform kernels.

However, as the size of the transform, that is, the size of a region towhich the transform is applied, may be, for example, a size other than8×8 or 4×4, the number of sets may be n, and the number of transformkernels in each set may be k.

The transform set may be referred to as an NSST set or an LFNST set. Aspecific set among the transform sets may be selected, for example,based on the intra prediction mode of the current block (CU orsubblock). A low-frequency non-separable transform (LFNST) may be anexample of a reduced non-separable transform, which will be describedlater, and represents a non-separable transform for a low frequencycomponent.

For reference, for example, the intra prediction mode may include twonon-directional (or non-angular) intra prediction modes and 65directional (or angular) intra prediction modes. The non-directionalintra prediction modes may include a planar intra prediction mode of No.0 and a DC intra prediction mode of No. 1, and the directional intraprediction modes may include 65 intra prediction modes of Nos. 2 to 66.However, this is an example, and this document may be applied even whenthe number of intra prediction modes is different. Meanwhile, in somecases, intra prediction mode No. 67 may be further used, and the intraprediction mode No. 67 may represent a linear model (LM) mode.

FIG. 6 exemplarily shows intra directional modes of 65 predictiondirections.

Referring to FIG. 6 , on the basis of intra prediction mode 34 having aleft upward diagonal prediction direction, the intra prediction modesmay be divided into intra prediction modes having horizontaldirectionality and intra prediction modes having verticaldirectionality. In FIG. 6 , H and V denote horizontal directionality andvertical directionality, respectively, and numerals−32 to 32 indicatedisplacements in 1/32 units on a sample grid position. These numeralsmay represent an offset for a mode index value. Intra prediction modes 2to 33 have the horizontal directionality, and intra prediction modes 34to 66 have the vertical directionality. Strictly speaking, intraprediction mode 34 may be considered as being neither horizontal norvertical, but may be classified as belonging to the horizontaldirectionality in determining a transform set of a secondary transform.This is because input data is transposed to be used for a verticaldirection mode symmetrical on the basis of intra prediction mode 34, andan input data alignment method for a horizontal mode is used for intraprediction mode 34. Transposing input data means that rows and columnsof two-dimensional M×N block data are switched into N×M data. Intraprediction mode 18 and intra prediction mode 50 may represent ahorizontal intra prediction mode and a vertical intra prediction mode,respectively, and intra prediction mode 2 may be referred to as a rightupward diagonal intra prediction mode because intra prediction mode 2has a left reference pixel and performs prediction in a right upwarddirection. Likewise, intra prediction mode 34 may be referred to as aright downward diagonal intra prediction mode, and intra prediction mode66 may be referred to as a left downward diagonal intra prediction mode.

According to an example, the four transform sets according to the intraprediction mode may be mapped, for example, as shown in the followingtable.

TABLE 2 lfnstPredModeIntra lfnstTrSetIdx lfnstPredModeIntra < 0 1 0 <=lfnstPredModeIntra <= 1 0  2 <= lfnstPredModeIntra <= 12 1 13 <=lfnstPredModeIntra <= 23 2 24 <= lfnstPredModeIntra <= 44 3 45 <=lfnstPredModeIntra <= 55 2 56 <= lfnstPredModeIntra <= 80 1 81 <=lfnstPredModeIntra <= 83 0

As shown in Table 2, any one of the four transform sets, that is,lfnstTrSetIdx, may be mapped to any one of four indexes, that is, 0 to3, according to the intra prediction mode.

When it is determined that a specific set is used for the non-separabletransform, one of k transform kernels in the specific set may beselected through a non-separable secondary transform index. An encodingapparatus may derive a non-separable secondary transform indexindicating a specific transform kernel based on a rate-distortion (RD)check and may signal the non-separable secondary transform index to adecoding apparatus. The decoding apparatus may select one of the ktransform kernels in the specific set based on the non-separablesecondary transform index. For example, lfnst index value 0 may refer toa first non-separable secondary transform kernel, lfnst index value 1may refer to a second non-separable secondary transform kernel, andlfnst index value 2 may refer to a third non-separable secondarytransform kernel. Alternatively, lfnst index value 0 may indicate thatthe first non-separable secondary transform is not applied to the targetblock, and lfnst index values 1 to 3 may indicate the three transformkernels.

The transformer may perform the non-separable secondary transform basedon the selected transform kernels, and may obtain modified (secondary)transform coefficients. As described above, the modified transformcoefficients may be derived as transform coefficients quantized throughthe quantizer, and may be encoded and signaled to the decoding apparatusand transferred to the dequantizer/inverse transformer in the encodingapparatus.

Meanwhile, as described above, if the secondary transform is omitted,(primary) transform coefficients, which are an output of the primary(separable) transform, may be derived as transform coefficientsquantized through the quantizer as described above, and may be encodedand signaled to the decoding apparatus and transferred to thedequantizer/inverse transformer in the encoding apparatus.

The inverse transformer may perform a series of procedures in theinverse order to that in which they have been performed in theabove-described transformer. The inverse transformer may receive(dequantized) transformer coefficients, and derive (primary) transformcoefficients by performing a secondary (inverse) transform (S550), andmay obtain a residual block (residual samples) by performing a primary(inverse) transform on the (primary) transform coefficients (S560). Inthis connection, the primary transform coefficients may be calledmodified transform coefficients from the viewpoint of the inversetransformer. As described above, the encoding apparatus and the decodingapparatus may generate the reconstructed block based on the residualblock and the predicted block, and may generate the reconstructedpicture based on the reconstructed block.

The decoding apparatus may further include a secondary inverse transformapplication determinator (or an element to determine whether to apply asecondary inverse transform) and a secondary inverse transformdeterminator (or an element to determine a secondary inverse transform).The secondary inverse transform application determinator may determinewhether to apply a secondary inverse transform. For example, thesecondary inverse transform may be an NSST, an RST, or an LFNST and thesecondary inverse transform application determinator may determinewhether to apply the secondary inverse transform based on a secondarytransform flag obtained by parsing the bitstream. In another example,the secondary inverse transform application determinator may determinewhether to apply the secondary inverse transform based on a transformcoefficient of a residual block.

The secondary inverse transform determinator may determine a secondaryinverse transform. In this case, the secondary inverse transformdeterminator may determine the secondary inverse transform applied tothe current block based on an LFNST (NSST or RST) transform setspecified according to an intra prediction mode. In an embodiment, asecondary transform determination method may be determined depending ona primary transform determination method. Various combinations ofprimary transforms and secondary transforms may be determined accordingto the intra prediction mode. Further, in an example, the secondaryinverse transform determinator may determine a region to which asecondary inverse transform is applied based on the size of the currentblock.

Meanwhile, as described above, if the secondary (inverse) transform isomitted, (dequantized) transform coefficients may be received, theprimary (separable) inverse transform may be performed, and the residualblock (residual samples) may be obtained. As described above, theencoding apparatus and the decoding apparatus may generate thereconstructed block based on the residual block and the predicted block,and may generate the reconstructed picture based on the reconstructedblock.

Meanwhile, in the present disclosure, a reduced secondary transform(RST) in which the size of a transform matrix (kernel) is reduced may beapplied in the concept of NSST in order to reduce the amount ofcomputation and memory required for the non-separable secondarytransform.

Meanwhile, the transform kernel, the transform matrix, and thecoefficient constituting the transform kernel matrix, that is, thekernel coefficient or the matrix coefficient, described in the presentdisclosure may be expressed in 8 bits. This may be a condition forimplementation in the decoding apparatus and the encoding apparatus, andmay reduce the amount of memory required to store the transform kernelwith a performance degradation that can be reasonably accommodatedcompared to the existing 9 bits or 10 bits. In addition, the expressingof the kernel matrix in 8 bits may allow a small multiplier to be used,and may be more suitable for single instruction multiple data (SIMD)instructions used for optimal software implementation.

In the present specification, the term “RST” may mean a transform whichis performed on residual samples for a target block based on a transformmatrix whose size is reduced according to a reduced factor. In the caseof performing the reduced transform, the amount of computation requiredfor transform may be reduced due to a reduction in the size of thetransform matrix. That is, the RST may be used to address thecomputational complexity issue occurring at the non-separable transformor the transform of a block of a great size.

RST may be referred to as various terms, such as reduced transform,reduced secondary transform, reduction transform, simplified transform,simple transform, and the like, and the name which RST may be referredto as is not limited to the listed examples. Alternatively, ince the RSTis mainly performed in a low frequency region including a non-zerocoefficient in a transform block, it may be referred to as aLow-Frequency Non-Separable Transform (LFNST). The transform index maybe referred to as an LFNST index.

Meanwhile, when the secondary inverse transform is performed based onRST, the inverse transformer 235 of the encoding apparatus 200 and theinverse transformer 322 of the decoding apparatus 300 may include aninverse reduced secondary transformer which derives modified transformcoefficients based on the inverse RST of the transform coefficients, andan inverse primary transformer which derives residual samples for thetarget block based on the inverse primary transform of the modifiedtransform coefficients. The inverse primary transform refers to theinverse transform of the primary transform applied to the residual. Inthe present disclosure, deriving a transform coefficient based on atransform may refer to deriving a transform coefficient by applying thetransform.

FIG. 7 is a diagram illustrating an RST according to an embodiment ofthe present disclosure.

In the present disclosure, a “target block” may refer to a current blockto be coded, a residual block, or a transform block.

In the RST according to an example, an N-dimensional vector may bemapped to an R-dimensional vector located in another space, so that thereduced transform matrix may be determined, where R is less than N. Nmay mean the square of the length of a side of a block to which thetransform is applied, or the total number of transform coefficientscorresponding to a block to which the transform is applied, and thereduced factor may mean an R/N value. The reduced factor may be referredto as a reduced factor, reduction factor, simplified factor, simplefactor or other various terms. Meanwhile, R may be referred to as areduced coefficient, but according to circumstances, the reduced factormay mean R. Further, according to circumstances, the reduced factor maymean the N/R value.

In an example, the reduced factor or the reduced coefficient may besignaled through a bitstream, but the example is not limited to this.For example, a predefined value for the reduced factor or the reducedcoefficient may be stored in each of the encoding apparatus 200 and thedecoding apparatus 300, and in this case, the reduced factor or thereduced coefficient may not be signaled separately.

The size of the reduced transform matrix according to an example may beR×N less than N×N, the size of a conventional transform matrix, and maybe defined as in Equation 4 below.

$\begin{matrix}{T_{R \times N} = \begin{bmatrix}t_{11} & t_{12} & t_{13} & \ldots & t_{1N} \\t_{21} & t_{22} & t_{23} & & t_{2N} \\ & \vdots & & \ddots & \vdots \\t_{R1} & t_{R2} & t_{R3} & \ldots & t_{RN}\end{bmatrix}} & \left\lbrack {{Equation}4} \right\rbrack\end{matrix}$

The matrix Tin the Reduced Transform block shown in FIG. 7(a) may meanthe matrix T_(R×N) of Equation 4. As shown in FIG. 7(a), when thereduced transform matrix T_(R×N) is multiplied to residual samples forthe target block, transform coefficients for the target block may bederived.

In an example, if the size of the block to which the transform isapplied is 8×8 and R=16 (i.e., R/N=16/64=1/4), then the RST according toFIG. 7(a) may be expressed as a matrix operation as shown in Equation 5below. In this case, memory and multiplication calculation can bereduced to approximately ¼ by the reduced factor.

In the present disclosure, a matrix operation may be understood as anoperation of multiplying a column vector by a matrix, disposed on theleft of the column vector, to obtain a column vector.

$\begin{matrix}{\begin{bmatrix}t_{1,1} & t_{1,2} & t_{1,3} & \ldots & t_{1,64} \\t_{2,1} & t_{2,2} & t_{2,3} & & t_{2,64} \\ & \vdots & & \ddots & \vdots \\t_{16,1} & t_{16,2} & t_{16,3} & \ldots & t_{16,64}\end{bmatrix} \times \begin{bmatrix}r_{1} \\r_{2} \\ \vdots \\r_{64}\end{bmatrix}} & \left\lbrack {{Equation}5} \right\rbrack\end{matrix}$

In Equation 5, r₁ to r₆₄ may represent residual samples for the targetblock and may be specifically transform coefficients generated byapplying a primary transform. As a result of the calculation of Equation5 transform coefficients ci for the target block may be derived, and aprocess of deriving ci may be as in Equation 6.

for i from to R:

c _(i)=0

-   -   for j from 1 to N

c _(i) +=t _(i,j) *r _(j)  [Equation 6]

As a result of the calculation of Equation 6, transform coefficients c₁to c_(R) for the target block may be derived. That is, when R=16,transform coefficients c₁ to c₁₆ for the target block may be derived.If, instead of RST, a regular transform is applied and a transformmatrix of 64×64 (N×N) size is multiplied to residual samples of 64×1(Nx1) size, then only 16 (R) transform coefficients are derived for thetarget block because RST was applied, although 64 (N) transformcoefficients are derived for the target block. Since the total number oftransform coefficients for the target block is reduced from N to R, theamount of data transmitted by the encoding apparatus 200 to the decodingapparatus 300 decreases, so efficiency of transmission between theencoding apparatus 200 and the decoding apparatus 300 can be improved.

When considered from the viewpoint of the size of the transform matrix,the size of the regular transform matrix is 64×64 (N×N), but the size ofthe reduced transform matrix is reduced to 16×64 (R×N), so memory usagein a case of performing the RST can be reduced by an R/N ratio whencompared with a case of performing the regular transform. In addition,when compared to the number of multiplication calculations N×N in a caseof using the regular transform matrix, the use of the reduced transformmatrix can reduce the number of multiplication calculations by the R/Nratio (R×N).

In an example, the transformer 232 of the encoding apparatus 200 mayderive transform coefficients for the target block by performing theprimary transform and the RST-based secondary transform on residualsamples for the target block. These transform coefficients may betransferred to the inverse transformer of the decoding apparatus 300,and the inverse transformer 322 of the decoding apparatus 300 may derivethe modified transform coefficients based on the inverse reducedsecondary transform (RST) for the transform coefficients, and may deriveresidual samples for the target block based on the inverse primarytransform for the modified transform coefficients.

The size of the inverse RST matrix T_(N×R) according to an example isN×R less than the size N×N of the regular inverse transform matrix, andis in a transpose relationship with the reduced transform matrix T_(R×N)shown in Equation 4.

The matrix T in the Reduced Inv. Transform block shown in FIG. 7(b) maymean the inverse RST matrix T_(R×N) ^(T) (the superscript T meanstranspose). When the inverse RST matrix TR, is multiplied to thetransform coefficients for the target block as shown in FIG. 7(b), themodified transform coefficients for the target block or the residualsamples for the current block may be derived. The inverse RST matrixT_(R×N) ^(T) may be expressed as (T_(R×N) ^(T))_(N×R).

More specifically, when the inverse RST is applied as the secondaryinverse transform, the modified transform coefficients for the targetblock may be derived when the inverse RST matrix T_(R×N) ^(T) ismultiplied to the transform coefficients for the target block.Meanwhile, the inverse RST may be applied as the inverse primarytransform, and in this case, the residual samples for the target blockmay be derived when the inverse RST matrix T_(R×N) ^(T) is multiplied tothe transform coefficients for the target block.

In an example, if the size of the block to which the inverse transformis applied is 8×8 and R=16 (i.e., R/N=16/64=1/4), then the RST accordingto FIG. 7(b) may be expressed as a matrix operation as shown in Equation7 below.

$\begin{matrix}{\begin{bmatrix}t_{1,1} & t_{2,1} & & t_{16,1} \\t_{1,2} & t_{2,2} & \ldots & t_{16,2} \\t_{1,3} & t_{2,3} & & t_{16,3} \\ \vdots & \vdots & & \vdots \\ & \vdots & \ddots & \vdots \\t_{1,64} & t_{2,64} & \ldots & t_{16,64}\end{bmatrix} \times \begin{bmatrix}c_{1} \\c_{2} \\ \vdots \\c_{16}\end{bmatrix}} & \left\lbrack {{Equation}7} \right\rbrack\end{matrix}$

In Equation 7, c₁ to c₁₆ may represent the transform coefficients forthe target block. As a result of the calculation of Equation 7, r_(i)representing the modified transform coefficients for the target block orthe residual samples for the target block may be derived, and theprocess of deriving r_(i) may be as in Equation 8.

for i from 1 to N:

r _(i)=0

-   -   for j from 1 to R

r _(i) +=t _(j,i) *c _(j)  [Equation 8]

As a result of the calculation of Equation 8, r, to r_(N) representingthe modified transform coefficients for the target block or the residualsamples for the target block may be derived. When considered from theviewpoint of the size of the inverse transform matrix, the size of theregular inverse transform matrix is 64×64 (N×N), but the size of thereduced inverse transform matrix is reduced to 64×16 (R×N), so memoryusage in a case of performing the inverse RST can be reduced by an R/Nratio when compared with a case of performing the regular inversetransform. In addition, when compared to the number of multiplicationcalculations N×N in a case of using the regular inverse transformmatrix, the use of the reduced inverse transform matrix can reduce thenumber of multiplication calculations by the R/N ratio (N×R).

A transform set configuration shown in Table 2 may also be applied to an8×8 RST. That is, the 8×8 RST may be applied according to a transformset in Table 2. Since one transform set includes two or three transforms(kernels) according to an intra prediction mode, it may be configured toselect one of up to four transforms including that in a case where nosecondary transform is applied. In a transform where no secondarytransform is applied, it may be considered to apply an identity matrix.Assuming that indexes 0, 1, 2, and 3 are respectively assigned to thefour transforms (e.g., index 0 may be allocated to a case where anidentity matrix is applied, that is, a case where no secondary transformis applied), a transform index or an lfnst index as a syntax element maybe signaled for each transform coefficient block, thereby designating atransform to be applied. That is, for a top-left 8×8 block, through thetransform index, it is possible to designate an 8×8 RST in an RSTconfiguration, or to designate an 8×8 lfnst when the LFNST is applied.The 8×8 lfnst and the 8×8 RST refer to transforms applicable to an 8×8region included in the transform coefficient block w % ben both W and Hof the target block to be transformed are equal to or greater than 8,and the 8×8 region may be a top-left 8×8 region in the transformcoefficient block. Similarly, a 4×4 lfnst and a 4×4 RST refer totransforms applicable to a 4×4 region included in the transformcoefficient block when both W and H of the target block to are equal toor greater than 4, and the 4×4 region may be a top-left 4×4 region inthe transform coefficient block.

According to an embodiment of the present disclosure, for a transform inan encoding process, only 48 pieces of data may be selected and amaximum 16×48 transform kernel matrix may be applied thereto, ratherthan applying a 16×64 transform kernel matrix to 64 pieces of dataforming an 8×8 region. Here, “maximum” means that m has a maximum valueof 16 in an m×48 transform kernel matrix for generating m coefficients.That is, when an RST is performed by applying an m×48 transform kernelmatrix (m≤16) to an 8×8 region, 48 pieces of data are input and mcoefficients are generated. When m is 16, 48 pieces of data are inputand 16 coefficients are generated. That is, assuming that 48 pieces ofdata form a 48×1 vector, a 16×48 matrix and a 48×1 vector aresequentially multiplied, thereby generating a 16×1 vector. Here, the 48pieces of data forming the 8×8 region may be properly arranged, therebyforming the 48×1 vector. For example, a 48×1 vector may be constructedbased on 48 pieces of data constituting a region excluding the bottomright 4×4 region among the 8×8 regions. Here, when a matrix operation isperformed by applying a maximum 16×48 transform kernel matrix, 16modified transform coefficients are generated, and the 16 modifiedtransform coefficients may be arranged in a top-left 4×4 regionaccording to a scanning order, and a top-right 4×4 region and abottom-left 4×4 region may be filled with zeros.

For an inverse transform in a decoding process, the transposed matrix ofthe foregoing transform kernel matrix may be used. That is, when aninverse RST or LFNST is performed in the inverse transform processperformed by the decoding apparatus, input coefficient data to which theinverse RST is applied is configured in a one-dimensional vectoraccording to a predetermined arrangement order, and a modifiedcoefficient vector obtained by multiplying the one-dimensional vectorand a corresponding inverse RST matrix on the left of theone-dimensional vector may be arranged in a two-dimensional blockaccording to a predetermined arrangement order.

In summary, in the transform process, when an RST or LFNST is applied toan 8×8 region, a matrix operation of 48 transform coefficients intop-left, top-right, and bottom-left regions of the 8×8 region excludingthe bottom-right region among transform coefficients in the 8×8 regionand a 16×48 transform kernel matrix. For the matrix operation, the 48transform coefficients are input in a one-dimensional array. When thematrix operation is performed, 16 modified transform coefficients arederived, and the modified transform coefficients may be arranged in thetop-left region of the 8×8 region.

On the contrary, in the inverse transform process, when an inverse RSTor LFNST is applied to an 8×8 region, 16 transform coefficientscorresponding to a top-left region of the 8×8 region among transformcoefficients in the 8×8 region may be input in a one-dimensional arrayaccording to a scanning order and may be subjected to a matrix operationwith a 48×16 transform kernel matrix. That is, the matrix operation maybe expressed as (48×16 matrix)*(16×1 transform coefficient vector)=(48×1modified transform coefficient vector). Here, an n×1 vector may beinterpreted to have the same meaning as an n×1 matrix and may thus beexpressed as an n×1 column vector. Further, * denotes matrixmultiplication. When the matrix operation is performed, 48 modifiedtransform coefficients may be derived, and the 48 modified transformcoefficients may be arranged in top-left, top-right, and bottom-leftregions of the 8×8 region excluding a bottom-right region.

When a secondary inverse transform is based on an RST, the inversetransformer 235 of the encoding apparatus 200 and the inversetransformer 322 of the decoding apparatus 300 may include an inversereduced secondary transformer to derive modified transform coefficientsbased on an inverse RST on transform coefficients and an inverse primarytransformer to derive residual samples for the target block based on aninverse primary transform on the modified transform coefficients. Theinverse primary transform refers to the inverse transform of a primarytransform applied to a residual. In the present disclosure, deriving atransform coefficient based on a transform may refer to deriving thetransform coefficient by applying the transform.

The above-described non-separated transform, the LFNST, will bedescribed in detail as follows. The LFNST may include a forwardtransform by the encoding apparatus and an inverse transform by thedecoding apparatus.

The encoding apparatus receives a result (or a part of a result) derivedafter applying a primary (core) transform as an input, and applies aforward secondary transform (secondary transform).

y=G ^(T) x  [Equation 9]

In Equation 9, x and y are inputs and outputs of the secondarytransform, respectively, and G is a matrix representing the secondarytransform, and transform basis vectors are composed of column vectors.In the case of an inverse LFNST, when the dimension of thetransformation matrix G is expressed as [number of rows×number ofcolumns], in the case of an forward LFNST, the transposition of matrix Gbecomes the dimension of G^(T).

For the inverse LFNST, the dimensions of matrix G are [48×16], [48×8],[16×16], [16×8], and the [48×8] matrix and the [16×8] matrix are partialmatrices that sampled 8 transform basis vectors from the left of the[48×16] matrix and the [16×16] matrix, respectively.

On the other hand, for the forward LFNST, the dimensions of matrix G^(T)are [16×48], [8×48], [16×16], [8×16], and the [8×48 matrix and the 8×16]matrix are partial matrices obtained by sampling 8 transform basisvectors from the top of the [16×48] matrix and the [16×16] matrix,respectively.

Therefore, in the case of the forward LFNST, a [48×1] vector or [16×1]vector is possible as an input x, and a [16×1] vector or a [8×1] vectoris possible as an output y. In video coding and decoding, the output ofthe forward primary transform is two-dimensional (2D) data, so toconstruct the [48×1] vector or the [16×1] vector as the input x, aone-dimensional vector must be constructed by properly arranging the 2Ddata that is the output of the forward transformation.

FIG. 8 is a diagram illustrating a sequence of arranging output data ofa forward primary transformation into a one-dimensional vector accordingto an example. The left diagrams of (a) and (b) of FIG. 8 show thesequence for constructing a [48×1] vector, and the right diagrams of (a)and (b) of FIG. 8 shows the sequence for constructing a [16×1] vector.In the case of the LFNST, a one-dimensional vector x can be obtained bysequentially arranging 2D data in the same order as in (a) and (b) ofFIG. 8 .

The arrangement direction of the output data of the forward primarytransform may be determined according to an intra prediction mode of thecurrent block. For example, when the intra prediction mode of thecurrent block is in the horizontal direction with respect to thediagonal direction, the output data of the forward primary transform maybe arranged in the order of (a) of FIG. 8 , and when the intraprediction mode of the current block is in the vertical direction withrespect to the diagonal direction, the output data of the forwardprimary transform may be arranged in the order of (b) of FIG. 8 .

According to an example, an arrangement order different from thearrangement orders of (a) and (b) FIG. 8 may be applied, and in order toderive the same result (y vector) as when the arrangement orders of (a)and (b) FIG. 8 is applied, the column vectors of the matrix G may berearranged according to the arrangement order. That is, it is possibleto rearrange the column vectors of G so that each element constitutingthe x vector is always multiplied by the same transform basis vector.

Since the output y derived through Equation 9 is a one-dimensionalvector, when two-dimensional data is required as input data in theprocess of using the result of the forward secondary transformation asan input, for example, in the process of performing quantization orresidual coding, the output y vector of Equation 9 must be properlyarranged as 2D data again.

FIG. 9 is a diagram illustrating a sequence of arranging output data ofa forward secondary transform into a two-dimensional block according toan example.

In the case of the LFNST, output values may be arranged in a 2D blockaccording to a predetermined scan order. (a) of FIG. 9 shows that whenthe output y is a [16×1] vector, the output values are arranged at 16positions of the 2D block according to a diagonal scan order. (b) ofFIG. 9 shows that when the output y is a [8×1] vector, the output valuesare arranged at 8 positions of the 2D block according to the diagonalscan order, and the remaining 8 positions are filled with zeros. X in(b) of FIG. 9 indicates that it is filled with zero.

According to another example, since the order in which the output vectory is processed in performing quantization or residual coding may bepreset, the output vector y may not be arranged in the 2D block as shownin FIG. 9 . However, in the case of the residual coding, data coding maybe performed in 2D block (eg, 4×4) units such as CG (Coefficient Group),and in this case, the data are arranged according to a specific order asin the diagonal scan order of FIG. 9 .

Meanwhile, the decoding apparatus may configure the one-dimensionalinput vector y by arranging two-dimensional data output through adequantization process or the like according to a preset scan order forthe inverse transformation. The input vector y may be output as theoutput vector x by the following equation.

x=Gy  [Equation 10]

In the case of the inverse LFNST, an output vector x can be derived bymultiplying an input vector y, which is a [16×1] vector or a [8×1]vector, by a G matrix. For the inverse LFNST, the output vector x can beeither a [48×1] vector or a [16×1] vector.

The output vector x is arranged in a two-dimensional block according tothe order shown in FIG. 8 and is arranged as two-dimensional data, andthis two-dimensional data becomes input data (or a part of input data)of the inverse primary transformation.

Accordingly, the inverse secondary transformation is the opposite of theforward secondary transformation process as a whole, and in the case ofthe inverse transformation, unlike in the forward direction, the inversesecondary transformation is first applied, and then the inverse primarytransformation is applied.

In the inverse LFNST, one of 8 [48×16] matrices and 8 [16×16] matricesmay be selected as the transformation matrix G. Whether to apply the[48×16] matrix or the [16×16] matrix depends on the size and shape ofthe block.

In addition, 8 matrices may be derived from four transform sets as shownin Table 2 above, and each transform set may consist of two matrices.Which transform set to use among the 4 transform sets is determinedaccording to the intra prediction mode, and more specifically, thetransform set is determined based on the value of the intra predictionmode extended by considering the Wide Angle Intra Prediction (WAIP).Which matrix to select from among the two matrices constituting theselected transform set is derived through index signaling. Morespecifically, 0, 1, and 2 are possible as the transmitted index value, 0may indicate that the LFNST is not applied, and 1 and 2 may indicate anyone of two transform matrices constituting a transform set selectedbased on the intra prediction mode value.

FIG. 9 is a diagram illustrating wide-angle intra prediction modesaccording to an embodiment of the present document.

The general intra prediction mode value may have values from 0 to 66 and81 to 83, and the intra prediction mode value extended due to WAIP mayhave a value from −14 to 83 as shown. Values from 81 to 83 indicate theCCLM (Cross Component Linear Model) mode, and values from −14 to −1 andvalues from 67 to 80 indicate the intra prediction mode extended due tothe WAIP application.

When the width of the prediction current block is greater than theheight, the upper reference pixels are generally closer to positionsinside the block to be predicted. Therefore, it may be more accurate topredict in the bottom-left direction than in the top-right direction.Conversely, when the height of the block is greater than the width, theleft reference pixels are generally close to positions inside the blockto be predicted. Therefore, it may be more accurate to predict in thetop-right direction than in the bottom-left direction. Therefore, it maybe advantageous to apply remapping, ie, mode index modification, to theindex of the wide-angle intra prediction mode.

When the wide-angle intra prediction is applied, information on theexisting intra prediction may be signaled, and after the information isparsed, the information may be remapped to the index of the wide-angleintra prediction mode. Therefore, the total number of the intraprediction modes for a specific block (eg, a non-square block of aspecific size) may not change, and that is, the total number of theintra prediction modes is 67, and intra prediction mode coding for thespecific block may not be changed.

Table 3 below shows a process of deriving a modified intra mode byremapping the intra prediction mode to the wide-angle intra predictionmode.

TABLE 3 Inputs to this process are: - a variable predModeIntraspecifying the intra prediction mode, - a variable nTbW specifying thetransform block width, - a variable nTbH specifying the transform blockheight, - a variable cIdx specifying the colour component of the currentblock. Output of this process is the modified intra prediction modepredModeIntra. The variables nW and nH are derived as follows: - IfIntraSubPartitionsSplitType is equal to ISP_NO_SPLIT or cIdx is notequal to 0, the following applies:  nW = nTbW  (8-97)  nH = nTbH (8-98) - Otherwise ( IntraSubPartitionsSplitType is not equal toISP_NO_SPLIT and cIdx is equal to 0 ), the following applies:  nW = nCbW (8-99)  nH = nCbH (8-100) The variable whRatio is set equal to Abs(Log2( nW / nH ) ). For non-square blocks (nW is set equal to nH), theintra prediction mode predModeIntra is modified as follows: - If all ofthe following conditions are true, predModeIntra is set equal to (predModeIntra + 65 ). - nW is greater than nH - predModeIntra is greaterthan or equal to 2 - predModeIntra is less than ( whRatio > 1 ) ? ( 8 +2 * whRatio ) : 8 - Otherwise, if all of the following conditions aretrue, predModeIntra is set equal to ( predModeIntra − 67 ). - nH isgreater than nW - predModeIntra is less than or equal to 66 -predModeIntra is greater than ( whRatio > 1 ) ? ( 60 − 2 * whRatio ) :60

In Table 3, the extended intra prediction mode value is finally storedin the predModelntra variable, and ISP_NO_SPLIT indicates that the CUblock is not divided into sub-partitions by the Intra Sub Partitions(ISP) technique currently adopted in the VVC standard, and the cIdxvariable Values of 0, 1, and 2 indicate the case of luma, Cb, and Crcomponents, respectively. Log 2 function shown in Table 3 returns a logvalue with a base of 2, and the Abs function returns an absolute value.

Variable predModeintra indicating the intra prediction mode and theheight and width of the transform block, etc. are used as input valuesof the wide angle intra prediction mode mapping process, and the outputvalue is the modified intra prediction mode predModeintra. The heightand width of the transform block or the coding block may be the heightand width of the current block for remapping of the intra predictionmode. At this time, the variable whRatio reflecting the ratio of thewidth to the width may be set to Abs(Log 2(nW/nH)).

For a non-square block, the intra prediction mode may be divided intotwo cases and modified.

First, if all conditions (1) (3) are satisfied, (1) the width of thecurrent block is greater than the height, (2) the intra prediction modebefore modifying is equal to or greater than 2, (3) the intra predictionmode is less than the value derived from (8+2*whRatio) when the variablewhRatio is greater than 1, and is less than 8 when the variable whRatiois less than or equal to 1 [predModeintra is less than(whRatio >1)?(8+2*whRatio):8], the intra prediction mode is set to avalue 65 greater than the intra prediction mode [predModelntra is setequal to (predModeIntra+65)].

If different from the above, that is, follow conditions (1)˜(3) aresatisfied, (1) the height of the current block is greater than thewidth, (2) the intra prediction mode before modifying is less than orequal to 66, (3) the intra prediction mode is greater than the valuederived from (60−2*whRatio) when the variable whRatio is greater than 1,and is greater than 60 when the variable whRatio is less than or equalto 1 [predModeintra is greater than (whRatio >1)?(60−2*whRatio):60], theintra prediction mode is set to a value 67 smaller than the intraprediction mode [predModelntra is set equal to (predModelntra−67)].

Table 2 above shows how a transform set is selected based on the intraprediction mode value extended by the WAIP in the LFNST. As shown inFIG. 10 , modes 14 to 33 and modes 35 to 80 are symmetric with respectto the prediction direction around mode 34. For example, mode 14 andmode 54 are symmetric with respect to the direction corresponding tomode 34. Therefore, the same transform set is applied to modes locatedin mutually symmetrical directions, and this symmetry is also reflectedin Table 2.

Meanwhile, it is assumed that forward LFNST input data for mode 54 issymmetrical with the forward LFNST input data for mode 14. For example,for mode 14 and mode 54, the two-dimensional data is rearranged intoone-dimensional data according to the arrangement order shown in (a) ofFIG. 8 and (b) of FIG. 8 , respectively. In addition, it can be seenthat the patterns in the order shown in (a) of FIG. 8 and (b) of FIG. 8are symmetrical with respect to the direction (diagonal direction)indicated by Mode 34.

Meanwhile, as described above, which transform matrix of the [48×16]matrix and the [16×16] matrix is applied to the LFNST is determined bythe size and shape of the transform target block.

FIG. 11 is a diagram illustrating a block shape to which the LFNST isapplied. (a) of FIG. 11 shows 4×4 blocks, (b) shows 4×8 and 8×4 blocks,(c) shows 4×N or N×4 blocks in which N is 16 or more, (d) shows 8×8blocks, (e) shows M×N blocks where M≥8, N≥8, and N>8 or M>8.

In FIG. 11 , blocks with thick borders indicate regions to which theLFNST is applied. For the blocks of FIGS. 13 (a) and (b), the LFNST isapplied to the top-left 4×4 region, and for the block of FIG. 11 (c),the LFNST is applied individually the two top-left 4×4 regions arecontinuously arranged. In (a), (b), and (c) of FIG. 11 , since the LFNSTis applied in units of 4×4 regions, this LFNST will be hereinafterreferred to as “4×4 LFNST”. Based on the matrix dimension for G, a[16×16] or [16×8] matrix may be applied.

More specifically, the [16×8] matrix is applied to the 4×4 block (4×4 TUor 4×4 CU) of FIG. 11 (a) and the [16×16] matrix is applied to theblocks in (b) and (c) of FIG. 11 . This is to adjust the computationalcomplexity for the worst case to 8 multiplications per sample.

With respect to (d) and (e) of FIG. 11 , the LFNST is applied to thetop-left 8×8 region, and this LFNST is hereinafter referred to as “8×8LFNST”. As a corresponding transformation matrix, a [48×16] matrix or[48×8] matrix may be applied. In the case of the forward LFNST, sincethe [48×1] vector (x vector in Equation 9) is input as input data, allsample values of the top-left 8×8 region are not used as input values ofthe forward LFNST. That is, as can be seen in the left order of FIG. 8(a) or the left order of FIG. 8 (b), the [48×1] vector may beconstructed based on samples belonging to the remaining 3 4×4 blockswhile leaving the bottom-right 4×4 block as it is.

The [48×8] matrix may be applied to an 8×8 block (8×8 TU or 8×8 CU) inFIG. 11 (d), and the [48×16] matrix may be applied to the 8×8 block inFIG. 11(e). This is also to adjust the computational complexity for theworst case to 8 multiplications per sample.

Depending on the block shape, when the corresponding forward LFNST (4×4LFNST or 8×8 LFNST) is applied, 8 or 16 output data (y vector inEquation 9, [8×1] or [16×1] vector) is generated. In the forward LFNST,the number of output data is equal to or less than the number of inputdata due to the characteristics of the matrix G^(T).

FIG. 12 is a diagram illustrating an arrangement of output data of aforward LFNST according to an example, and shows a block in which outputdata of the forward LFNST is arranged according to a block shape.

The shaded area at the top-left of the block shown in FIG. 12corresponds to the area where the output data of the forward LFNST islocated, the positions marked with 0 indicate samples filled with 0values, and the remaining area represents regions that are not changedby the forward LFNST. In the area not changed by the LFNST, the outputdata of the forward primary transform remains unchanged.

As described above, since the dimension of the transform matrix appliedvaries according to the shape of the block, the number of output dataalso varies. As FIG. 12 , the output data of the forward LFNST may notcompletely fill the top-left 4×4 block. In the case of (a) and (d) ofFIG. 12 , a [16×8] matrix and a [48×8] matrix are applied to the blockindicated by a thick line or a partial region inside the block,respectively, and a [8×1] vector as the output of the forward LFNST isgenerated. That is, according to the scan order shown in (b) of FIG. 9 ,only 8 output data may be filled as shown in (a) and (d) of FIG. 12 ,and 0 may be filled in the remaining 8 positions. In the case of theLFNST applied block of FIG. 11 (d), as shown in FIG. 12(d), two 4×4blocks in the top-right and bottom-left adjacent to the top-left 4×4block are also filled with 0 values.

As described above, basically, by signaling the LFNST index, whether toapply the LFNST and the transform matrix to be applied are specified. Asshown FIG. 12 , when the LFNST is applied, since the number of outputdata of the forward LFNST may be equal to or less than the number ofinput data, a region filled with a zero value occurs as follows.

1) As shown in (a) of FIG. 12 , samples from the 8th and later positionsin the scan order in the top-left 4×4 block, that is, samples from the9th to the 16th.

2) As shown in (d) and (e) of FIG. 12 , when the [48×16] matrix or the[48×8] matrix is applied, two 4×4 blocks adjacent to the top-left 4×4block or the second and third 4×4 blocks in the scan order.

Therefore, if non-zero data exists by checking the areas 1) and 2), itis certain that the LFNST is not applied, so that the signaling of thecorresponding LFNST index can be omitted.

According to an example, for example, in the case of LFNST adopted inthe VVC standard, since signaling of the LFNST index is performed afterthe residual coding, the encoding apparatus may know whether there isthe non-zero data (significant coefficients) for all positions withinthe TU or CU block through the residual coding. Accordingly, theencoding apparatus may determine whether to perform signaling on theLFNST index based on the existence of the non-zero data, and thedecoding apparatus may determine whether the LFNST index is parsed. Whenthe non-zero data does not exist in the area designated in 1) and 2)above, signaling of the LFNST index is performed.

Meanwhile, for the adopted LFNST, the following simplification methodsmay be applied.

(i) According to an example, the number of output data for the forwardLFNST may be limited to a maximum of 16.

In the case of (c) of FIG. 11 , the 4×4 LFNST may be applied to two 4×4regions adjacent to the top-left, respectively, and in this case, amaximum of 32 LFNST output data may be generated, when the number ofoutput data for forward LFNST is limited to a maximum of 16, in the caseof 4×N/Nx4 (N≥16) blocks (TU or CU), the 4×4 LFNST is only applied toone 4×4 region in the top-left, the LFNST may be applied only once toall blocks of FIG. 11 . Through this, the implementation of image codingmay be simplified.

(ii) According to an example, zero-out may be additionally applied to aregion to which the LFNST is not applied. In this document, the zero-outmay mean filling values of all positions belonging to a specific regionwith a value of 0. That is, the zero-out can be applied to a region thatis not changed due to the LFNST and maintains the result of the forwardprimary transformation. As described above, since the LFNST is dividedinto the 4×4 LFNST and the 8×8 LFNST, the zero-out can be divided intotwo types ((ii)-(A) and (ii)-(B)) as follows.

(ii)-(A) When the 4×4 LFNST is applied, a region to which the 4×4 LFNSTis not applied may be zeroed out. FIG. 13 is a diagram illustrating thezero-out in a block to which the 4×4 LFNST is applied according to anexample.

As shown in FIG. 13 , with respect to a block to which the 4×4 LFNST isapplied, that is, for all of the blocks in (a), (b) and (c) of FIG. 12 ,the whole region to which the LFNST is not applied may be filled withzeros.

On the other hand. (d) of FIG. 13 shows that when the maximum value ofthe number of the output data of the forward LFNST is limited to 16according to one example, the zero-out is performed on the remainingblocks to which the 4×4 LFNST is not applied.

(ii)-(B) When the 8×8 LFNST is applied, a region to which the 8×8 LFNSTis not applied may be zeroed out. FIG. 14 is a diagram illustrating thezero-out in a block to which the 8×8 LFNST is applied according to anexample.

As shown in FIG. 14 , with respect to a block to which the 8×8 LFNST isapplied, that is, for all of the blocks in (d) and (e) of FIG. 12 , thewhole region to which the LFNST is not applied may be filled with zeros.

(iii) Due to the zero-out presented in (ii) above, the area filled withzeros may be not same when the LFNST is applied. Accordingly, it ispossible to check whether the non-zero data exists according to thezero-out proposed in (ii) over a wider area than the case of the LFNSTof FIG. 12 .

For example, when (ii)-(B) is applied, after checking whether thenon-zero data exists where the area filled with zero values in (d) and(e) of FIG. 12 in addition to the area filled with 0 additionally inFIG. 14 , signaling for the LFNST index can be performed only when thenon-zero data does not exist.

Of course, even if the zero-out proposed in (ii) is applied, it ispossible to check whether the non-zero data exists in the same way asthe existing LFNST index signaling. That is, after checking whether thenon-zero data exists in the block filled with zeros in FIG. 12 , theLFNST index signaling may be applied. In this case, the encodingapparatus only performs the zero out and the decoding apparatus does notassume the zero out, that is, checking only whether the non-zero dataexists only in the area explicitly marked as 0 in FIG. 12 , may performthe LFN ST index parsing.

Various embodiments in which combinations of the simplification methods((i), (ii)-(A), (ii)-(B), (iii)) for the LFNST are applied may bederived. Of course, the combinations of the above simplification methodsare not limited to the following embodiment, and any combination may beapplied to the LFNST.

Embodiment

-   -   Limit the number of output data for forward LFNST to a maximum        of 16→(i)    -   When the 4×4 LFNST is applied, all areas to which the 4×4 LFNST        is not applied are zero-out→(ii)-(A)    -   When the 8×8 LFNST is applied, all areas to which the 8×8 LFNST        is not applied are zero-out→(ii)-(B)    -   After checking whether the non-zero data exists also the        existing area filled with zero value and the area filled with        zeros due to additional zero outs ((ii)-(A), (ii)-(B)), the        LFNST index is signaled only when the non-zero data does not        exist→(iii)

In the case of Embodiment, when the LFNST is applied, an area in whichthe non-zero output data can exist is limited to the inside of thetop-left 4×4 area. In more detail, in the case of FIG. 13 (a) and FIG.14 (a), the 8th position in the scan order is the last position wherenon-zero data can exist. In the case of FIGS. 13 (b) and (c) and FIG. 14(b), the 16th position in the scan order (ie, the position of thebottom-right edge of the top-left 4×4 block) is the last position wheredata other than 0 may exist.

Therefore, when the LFNST is applied, after checking whether thenon-zero data exists in a position where the residual coding process isnot allowed (at a position beyond the last position), it can bedetermined whether the LFNST index is signaled.

In the case of the zero-out method proposed in (ii), since the number ofdata finally generated when both the primary transform and the LFNST areapplied, the amount of computation required to perform the entiretransformation process can be reduced. That is, when the LFNST isapplied, since zero-out is applied to the forward primary transformoutput data existing in a region to which the LFNST is not applied,there is no need to generate data for the region that become zero-outduring performing the forward primary transform. Accordingly, it ispossible to reduce the amount of computation required to generate thecorresponding data. The additional effects of the zero-out methodproposed in (ii) are summarized as follows.

First, as described above, the amount of computation required to performthe entire transform process is reduced.

In particular, when (ii)-(B) is applied, the amount of calculation forthe worst case is reduced, so that the transform process can belightened. In other words, in general, a large amount of computation isrequired to perform a large-size primary transformation. By applying(ii)-(B), the number of data derived as a result of performing theforward LFNST can be reduced to 16 or less. In addition, as the size ofthe entire block (TU or CU) increases, the effect of reducing the amountof transform operation is further increased.

Second, the amount of computation required for the entire transformprocess can be reduced, thereby reducing the power consumption requiredto perform the transform.

Third, the latency involved in the transform process is reduced.

The secondary transformation such as the LFNST adds a computationalamount to the existing primary transformation, thus increasing theoverall delay time involved in performing the transformation. Inparticular, in the case of intra prediction, since reconstructed data ofneighboring blocks is used in the prediction process, during encoding,an increase in latency due to a secondary transformation leads to anincrease in latency until reconstruction. This can lead to an increasein overall latency of intra prediction encoding.

However, if the zero-out suggested in (ii) is applied, the delay time ofperforming the primary transform can be greatly reduced when LFNST isapplied, the delay time for the entire transform is maintained orreduced, so that the encoding apparatus can be implemented more simply.

Meanwhile, in the conventional intra prediction, a coding target blockis regarded as one coding unit, and coding is performed withoutpartition thereof. However, the ISP (Intra Sub-Partitions) coding refersto performing the intra prediction coding with the coding target blockbeing partitioned in a horizontal direction or a vertical direction. Inthis case, a reconstructed block may be generated by performingencoding/decoding in units of partitioned blocks, and the reconstructedblock may be used as a reference block of the next partitioned block.According to an example, in the ISP coding, one coding block may bepartitioned into two or four sub-blocks and be coded, and in the ISP,intra prediction is performed on one sub-block by referring to thereconstructed pixel value of a sub-block located adjacent to the left ortop side thereof. Hereinafter, the term “coding” may be used as aconcept including both coding performed by the encoding apparatus anddecoding performed by the decoding apparatus.

The ISP partitions a block predicted as luma intra into two or foursub-partitionings in a vertical direction or a horizontal directionaccording to the size of the block. For example, the minimum block sizeto which the ISP can be applied is 4×8 or 8×4. If the block size isgreater than 4×8 or 8×4, the block is partitioned into foursub-partitionings.

When the ISP is applied, the sub-blocks are sequentially coded accordingto the partition type, such as, horizontally or vertically, from left toright, or from top to bottom, and coding for the next sub-block may beperformed after performing up to a restoration process through inversetransform and intra prediction for one sub-block. For the leftmost oruppermost sub-block, as in a conventional intra prediction method, thereconstructed pixel of the coding block which has been already coded isreferred to. Additionally, if the previous sub-block is not adjacent toeach side of an internal sub-block that follows it, in order to derivereference pixels adjacent to a corresponding side, as in theconventional intra prediction method, the reconstructed pixel of analready coded adjacent coding block is referred to.

In the ISP coding mode, all sub-blocks may be coded with the same intraprediction mode, and a flag indicating whether or not to use the ISPcoding and a flag indicating in which direction (horizontal or vertical)partition is to be performed may be signaled. At this time, the numberof sub-blocks may be adjusted to 2 or 4 depending on the block shape,and when the size (width×height) of one sub-block is less than 16, thepartition may not be allowed for the corresponding sub-blocks, nor theapplication of the ISP coding itself may be restricted.

Meanwhile, in the case of ISP prediction mode, one coding unit ispartitioned into two or four partition blocks, that is, sub-blocks, andpredicted, and the same intra prediction mode is applied to the thuspartitioned two or four partition blocks.

As described above, both a horizontal direction (if an M×N coding unithaving a horizontal length and a vertical length of M and N,respectively, is divided in the horizontal direction, it is divided intoM×(N/2) blocks when divided into two, and into an M×(N/4) blocks whendivided into four) and a vertical direction (if the M×N coding unit isdivided in the vertical direction, it is divided into (M/2)×N blockswhen divided into two, and divided into (M/4)×N blocks when divided intofour) are possible as the partition direction. When partitioned in thehorizontal direction, partition blocks are coded in an order from top todown, and when partitioned in the vertical direction, partition blocksare coded in an order from left to right. The currently coded partitionblock may be predicted by referring to the reconstructed pixel values ofthe top (left) partition block in the case of the horizontal (vertical)direction partition.

Transformation may be applied to the residual signal generated by theISP prediction method in units of partition blocks. MTS (MultipleTransform Selection) technology based on the DST-7/DCT-8 combination aswell as the existing DCT-2 may be applied to the primary transform (coretransform or primary transform) based on the forward direction, and anLFNST (Low Frequency Non-Separable Transform) may be applied to atransform coefficient generated according to the primary transform togenerate a final modified transform coefficient.

That is, LFNST may also be applied to partition blocks divided byapplying the ISP prediction mode, and the same intra prediction mode isapplied to the divided partition blocks as described above. Accordingly,when selecting the LFNST set derived based on the intra prediction mode,the derived LFNST set may be applied to all partition blocks. That is,the same intra prediction mode is applied to all partition blocks, andthereby the same LFNST set may be applied to all partition blocks.

Meanwhile, according to an example, the LFNST may be applied only totransform blocks having both a horizontal and vertical length of 4 ormore. Therefore, when the horizontal or vertical length of the partitionblock partitioned according to the ISP prediction method is less than 4,the LFNST is not applied and the LFNST index is not signaled.Additionally, when the LFNST is applied to each partition block, thecorresponding partition block may be regarded as one transform block. Ofcourse, when the ISP prediction method is not applied, the LFNST may beapplied to the coding block.

Application of the LFNST to each partition block is described in detailas follows.

According to an example, after applying the forward LFNST to anindividual partition block, and after leaving only up to 16 coefficients(8 or 16) in the top-left 4×4 region according to the transformcoefficient scanning order, zero-out of filling all remaining positionsand regions with a value of 0 may be applied.

Alternatively, according to an example, when the length of one side ofthe partition block is 4, the LFNST is applied only to the top-left 4×4region, and when the length of all sides of the partition block, thatis, the width and height, are 8 or more, the LFNST may be applied to theremaining 48 coefficients except for a bottom-right 4×4 region in atop-left 8×8 region.

Alternatively, according to an example, in order to adjust thecomputational complexity of the worst case to 8 multiplications persample, when each partition block is 4×4 or 8×8, only 8 transformcoefficients may be output after applying the forward LFNST. That is, ifthe partition block is 4×4, an 8×16 matrix may be applied as a transformmatrix, and if the partition block is 8×8, an 8×48 matrix may be appliedas a transform matrix.

Meanwhile, in the current VVC standard, LFNST index signaling isperformed in units of coding units. Accordingly, when the ISP predictionmode is used and the LFNST is applied to all partition blocks, then thesame LFNST index value may be applied to the corresponding partitionblocks. That is, when the LFNST index value is transmitted once at thecoding unit level, the corresponding LFNST index may be applied to allpartition blocks in the coding unit. As described above, the LFNST indexvalue may have values of 0, 1, and 2, 0 indicates a case in which theLFNST is not applied, and 1 and 2 indicate two transform matricespresent in one LFNST set when the LFNST is applied.

As described above, the LFNST set is determined by the intra predictionmode, and since all partition blocks in the coding unit are predicted inthe same intra prediction mode in the case of the ISP prediction mode,the partition blocks may refer to the same LFNST set.

As another example, the LFNST index signaling is still performed inunits of coding units, but in the case of the ISP prediction mode,without determining whether or not to apply the LFNST uniformly to allpartition blocks, whether to apply the LFNST index value signaled at thecoding unit level to each partition block or not to apply the LFNST maybe determined through a separate condition. Here, the separate conditionmay be signaled in the form of a flag for each partition block throughthe bitstream, and when the flag value is 1, the LFNST index valuesignaled at the coding unit level may be applied, and when the flagvalue is 0, the LFNST may not be applied.

Hereinafter, a method for maintaining the computational complexity forthe worst case when LFNST is applied to the ISP mode will be described.

In the case of ISP mode, in order to maintain the number ofmultiplications per sample (or per coefficient, or per position) at acertain value or less when LFNST is applied, the application of LFNSTmay be restricted. Depending on the size of the partition block, thenumber of multiplications per sample (or per coefficient, or perposition) may be maintained at 8 or less by applying LFNST as follows.

1. When both the horizontal length and the vertical length of thepartition block are equal to or greater than 4, the same method as thecalculation complexity adjustment method for the worst case for LFNST inthe current VVC standard may be applied.

That is, when the partition block is a 4×4 block, instead of a 16×16matrix, in the forward direction, an 8×16 matrix obtained by samplingthe top 8 rows from a 16×16 matrix may be applied, and in the backwarddirection, a 16×8 matrix obtained by sampling the left 8 columns from a16×16 matrix may be applied. Additionally, when the partition block isan 8×8 block, in the forward direction, instead of a 16×48 matrix, an8×48 matrix obtained by sampling the top 8 rows from a 16×48 matrix maybe applied, and in the backward direction, instead of a 48×16 matrix, a48×8 matrix obtained by sampling the left 8 columns from a 48×16 matrixmay be applied.

In the case of a 4×N or N×4 (N>4) block, when forward transform isperformed, 16 coefficients generated after applying a 16×16 matrix onlyto the top-left 4×4 block are arranged in the top-left 4×4 region, andthe other regions may be filled with 0 values. Additionally, whenperforming inverse transform, 16 coefficients located in the top-left4×4 block may be arranged in the scanning order to configure an inputvector, and then 16 output data may be generated by multiplying the16×16 matrix. The generated output data may be arranged in the top-left4×4 region, and the remaining regions except for the top-left 4×4 regionmay be filled with zeros.

In the case of an 8×N or N×8 (N>8) block, when the forwardtransformation is performed, 16 coefficients generated after applyingthe 16×48 matrix only to the ROI region in the top-left 8×8 block(remaining regions excluding the bottom-right 4×4 block from thetop-left 8×8 block) may be arranged in the top-left 4×4 area, and theother regions may be filled with 0 values. Additionally, when performinginverse transform, 16 coefficients located in the top-left 4×4 block maybe arranged in the scanning order to configure an input vector, and then48 output data may be generated by multiplying the 48×16 matrix. Thegenerated output data may be filled in the ROI region, and the otherregions may be filled with 0 values.

As another example, in order to maintain the number of multiplicationsper sample (or per coefficient, or per position) at a certain value orless, the number of multiplications per sample (or per coefficient, orper position) based on the ISP coding unit size rather than the size ofthe ISP partition block may be maintained at 8 or less. If there is onlyone block among the ISP partition blocks, which satisfies the conditionunder which the LFNST is applied, the complexity calculation for theworst case of LFNST may be applied based on the corresponding codingunit size rather than the size of the partition block. For example, whena luma coding block for a certain coding unit is partitioned into 4partition blocks of 4×4 size and coded by the ISP, and when no non-zerotransform coefficient exists for two partition blocks among them, theother two partition blocks may be respectively set to generate 16transform coefficients instead of 8 (based on the encoder).

Hereinafter, a method of signaling the LFNST index in the case of theISP mode will be described.

As described above, the LFNST index may have values of 0, 1, and 2,where 0 indicates that the LFNST is not applied, and 1 and 2respectively indicate either one of two LFNST kernel matrices includedin the selected LFNST set. The LFNST is applied based on the LFNSTkernel matrix selected by the LFNST index. A method of transmitting theLFNST index in the current VVC standard will be described as follows.

1. An LFNST index may be transmitted once for each coding unit (CU), andin the case of a dual-tree, individual LFNST indexes may be signaled fora luma block and a chroma block, respectively.

2. When the LFNST index is not signaled, the LFNST index value isinferred to be a default value of 0. The case where the LFNST indexvalue is inferred to be 0 is as follows.

A. In the case of a mode in which no transform is applied (e.g.,transform skip, BDPCM, lossless coding, etc.)

B. When the primary transform is not DCT-2 (DST7 or DCT8), that is, whenthe transform in the horizontal direction or the transform in thevertical direction is not DCT-2

C. When the horizontal length or vertical length for the luma block ofthe coding unit exceeds the size of the transformable maximum lumatransform, for example, when the size of the transformable maximum lumatransform is 64, and when the size for the luma block of the codingblock is equal to 128×16, the LFNST cannot be applied.

In the case of the dual tree, it is determined whether or not the sizeof the maximum luma transform is exceeded for each of the coding unitfor the luma component and the coding unit for the chroma component.That is, it is checked for the luma block whether or not the size of themaximum transformable luma transform is exceeded, and it is checked forthe chroma block whether or not the horizontal/vertical length of thecorresponding luma block for the color format and the size of themaximum transformable luma transform exceed the size are exceeded. Forexample, when the color format is 4:2:0, the horizontal/vertical lengthof the corresponding luma block is twice that of the correspondingchroma block, and the transform size of the corresponding luma block istwice that of the corresponding chroma block. As another example, whenthe color format is 4:4:4, the horizontal/vertical length and transformsize and of the corresponding luma block are the same as those of thecorresponding chroma block.

A 64-length transform or a 32-length transform may mean a transformapplied to width or height having a length of 64 or 32, respectively,and “transform size” may mean 64 or 32 as the corresponding length.

In the case of a single tree, after checking whether or not a horizontallength or a vertical length of a luma block exceeds the maximumtransformable luma transform block size, if it exceeds, the LFNST indexsignaling may be omitted.

D. The LFNST index may be transmitted only when both the horizontallength and the vertical length of the coding unit are equal to orgreater than 4.

In the case of a dual tree, the LFNST index may be signaled only whenboth the horizontal and vertical lengths for a corresponding component(i.e., a luma or chroma component) are equal to or greater than 4.

In the case of a single tree, the LFNST index may be signaled when boththe horizontal and vertical lengths for the luma component are equal toor greater than 4.

E. If the position of the last non-zero coefficient is not a DC position(top-left position of the block), and if the position of the lastnon-zero coefficient is not a DC position, in the case of a luma blockof a dual tree type, the LFNST index is transmitted. In the case of adual tree type chroma block, if any one of the position of the lastnon-zero coefficient for Cb and the position of the last non-zerocoefficient for Cr is not a DC position, the corresponding LNFST indexis transmitted.

In the case of the single tree type, if the position of the lastnon-zero coefficient of any one of the luma component, Cb component, andCr component is not the DC position, the LFNST index is transmitted.

Here, if a coded block flag (CBF) value indicating whether or not atransform coefficient for one transform block exists is 0, the positionof the last non-zero coefficient for the corresponding transform blockis not checked in order to determine whether or not the LFNST index issignaled. That is, when the corresponding CBF value is 0, since notransform is applied to the corresponding block, the position of thelast non-zero coefficient may not be considered when checking thecondition for the LFNST index signaling.

For example, 1) in the case of a dual tree type and a luma component, ifthe corresponding CBF value is 0, the LFNST index is not signaled, 2) inthe case of a dual tree type and chroma component, if the CBF value forCb is 0 and the CBF value for Cr is 1, only the position of the lastnon-zero coefficient for Cr is checked and the corresponding LFNST indexis transmitted, 3) in the case of a single tree type, the position ofthe last non-zero coefficient is checked only for components having aCBF value of 1 for each of luma, Cb, and Cr.

F. When it is confirmed that the transform coefficient exists at aposition other than a position where the LFNST transform coefficient mayexist, the LFNST index signaling may be omitted. In the case of a 4×4transform block and an 8×8 transform block, LFNST transform coefficientsmay exist at eight positions from the DC position according to thetransform coefficient scanning order in the VVC standard, and theremaining positions are filled with zeros. Additionally, when the 4×4transform block and the 8×8 transform block are not, LFNST transformcoefficients may exist in sixteen positions from the DC positionaccording to the transform coefficient scanning order in the VVCstandard, and the remaining positions are filled with zeros.

Accordingly, if the non-zero transform coefficients exists in the regionwhich should be filled with the zero value after progressing theresidual coding, the LFNST index signaling may be omitted.

Meanwhile, the ISP mode may also be applied only to the luma block, ormay be applied to both the luma block and the chroma block. As describedabove, when ISP prediction is applied, the corresponding coding unit maybe divided into two or four partition blocks and predicted, and atransform may be applied to each of the partition blocks. Therefore,also when determining a condition for signaling the LFNST index in unitsof coding units, it is necessary to take into consideration the factthat the LFNST may be applied to respective partition blocks. Inaddition, when the ISP prediction mode is applied only to a specificcomponent (e.g., a luma block), the LFNST index must be signaled inconsideration of the fact that only the component is divided intopartition blocks. The LFNST index signaling methods available in the ISPmode are summarized as follows.

An LFNST index may be transmitted once for each coding unit (CU), and inthe case of a dual-tree, individual LFNST indexes may be signaled for aluma block and a chroma block, respectively.

2. When the LFNST index is not signaled, the LFNST index value isinferred to be a default value of 0. The case where the LFNST indexvalue is inferred to be 0 is as follows.

A. In the case of a mode in which no transform is applied (e.g.,transform skip, BDPCM, lossless coding, etc.)

B. When the horizontal length or vertical length for the luma block ofthe coding unit exceeds the size of the transformable maximum lumatransform, for example, when the size of the transformable maximum lumatransform is 64, and when the size for the luma block of the codingblock is equal to 128×16, the LFNST cannot be applied.

Whether or not to signal the LFNST index may be determined based on thesize of the partition block instead of the coding unit. That is, if thehorizontal or vertical length of the partition block for thecorresponding luma block exceeds the size of the transformable maximumluma transformation, the LFNST index signaling may be omitted and theLFNST index value may be inferred to be 0.

In the case of the dual tree, it is determined whether or not the sizeof the maximum luma transform is exceeded for each of the coding unit orpartition block for the luma component and the coding unit or partitionblock for the chroma component. That is, if the horizontal and verticallengths of the coding unit or partition block for luma are compared withthe maximum luma transform size, respectively, and at least one of themis greater than the maximum luma transform size, the LFNST is notapplied, and in the case of a coding unit or partition block for chroma,the horizontal/vertical length of the corresponding luma block for thecolor format and the size of the maximum transformable luma transformare compared. For example, when the color format is 4:2:0, thehorizontal/vertical length of the corresponding luma block is twice thatof the corresponding chroma block, and the transform size of thecorresponding luma block is twice that of the corresponding chromablock. As another example, when the color format is 4:4:4, thehorizontal/vertical length and transform size and of the correspondingluma block are the same as those of the corresponding chroma block.

In the case of a single tree, after checking whether or not a horizontallength or a vertical length for a luma block (coding unit or partitionblock) exceeds the maximum transformable luma transform block size, ifit exceeds, the LFNST index signaling may be omitted.

C. If the LFNST included in the current VVC standard is applied, theLFNST index may be transmitted only when both the horizontal length andthe vertical length of the partition block are equal to or greater than4.

If the LFNST for the 2×M(1×M) or M×2 (M×1) block is applied in additionto the LFNST included in the current VVC standard, the LFNST index maybe transmitted only when the size of the partition block is equal to orlarger than a 2×M(1×M) or M×2(M×1) block. Here, the expression “the P×Qblock is equal to or greater than the R×S block” means that P≥R and Q≥S.

In summary, the LFNST index can be transmitted only when the partitionblock is equal to or greater than the minimum size to which the LFNST isapplicable. In the case of a dual tree, the LFNST index can be signaledonly when the partition block for the luma or chroma component is equalto or larger than the minimum size to which the LFNST is applicable. Inthe case of a single tree, the LFNST index can be signaled only when thepartition block for the luma component is equal to or larger than theminimum size to which LFNST is applicable.

In this document, the expression “the M×N block is greater than or equalto the K×L block” means that M is greater than or equal to K and N isgreater than or equal to L. The expression “the M×N block is larger thanthe K×L block” means that M is greater than or equal to K and N isgreater than or equal to L, and that M is greater than K or N is greaterthan L. The expression “the M×N block less than or equal to the K×Lblock” means that M is less than or equal to K and N is less than orequal to L, while the expression “the M×N block is smaller than the K×Lblock” means that M is less than or equal to K and N is less than orequal to L, and that M is less than K or N is less than L.

D. If the position of the last non-zero coefficient is not a DC position(top-left position of the block), and if the position of the lastnon-zero coefficient is not a DC position in any one of all partitionblocks. In the case of a dual tree type luma block, the LFNST index istransmitted. In the case of a dual tree type and a chroma block, if atleast one of the position of the last non-zero coefficient of allpartition blocks for Cb (if the ISP mode is not applied to the chromacomponent, the number of partition blocks is considered to be one) andthe position of the last non-zero coefficient of all partition blocksfor Cr (if the ISP mode is not applied to the chroma component, thenumber of partition blocks is considered to be one) is not a DCposition, the corresponding LNFST index may be transmitted.

In the case of the single tree type, if the position of the lastnon-zero coefficient of any one of all partition blocks for the lumacomponent, the Cb component and the Cr component is not the DC position,the corresponding LFNST index may be transmitted.

Here, if the value of the coded block flag (CBF) indicating whether atransform coefficient exists for each partition block is 0, the positionof the last non-zero coefficient for the corresponding partition blockis not checked in order to determine whether or not the LFNST index issignaled. That is, when the corresponding CBF value is 0, since notransform is applied to the corresponding block, the position of thelast non-zero coefficient for the corresponding partition block is notconsidered when checking the condition for the LFNST index signaling.

For example, 1) in the case of a dual tree type and a luma component, ifthe corresponding CBF value for each partition block is 0, the partitionblock is excluded when determining whether or not to signal the LFNSTindex, 2) in the case of a dual tree type and a chroma component, if theCBF value for Cb is 0 and the CBF value for Cr is 1 for each partitionblock, only the position of the last non-zero coefficient for Cr ischecked to determine whether or not to signal the LFNST index, 3) in thecase of the single tree type, it is possible to determine whether or notto signal the LFNST index by checking the position of the last non-zerocoefficient only for blocks having a CBF value of 1 for all partitionblocks of the luma component, the Cb component, and the Cr component.

In the case of the ISP mode, image information may also be configured sothat the position of the last non-zero coefficient is not checked, andan embodiment thereof is as follows.

i. In the case of the ISP mode, the LFNST index signaling may be allowedwithout checking the position of the last non-zero coefficient for boththe luma block and the chroma block. That is, even if the position ofthe last non-zero coefficient for all partition blocks is the DCposition or the corresponding CBF value is 0, the LFNST index signalingmay be allowed.

ii. In the case of the ISP mode, the checking of the position of thelast non-zero coefficient only for the luma block may be omitted, and inthe case of the chroma block, the checking of the position of the lastnon-zero coefficient may be performed in the above-described manner. Forexample, in the case of a dual tree type and a luma block, the LFNSTindex signaling is allowed without checking the position of the lastnon-zero coefficient, and in the case of a dual tree type and a chromablock, whether or not a corresponding LFNST index is signaled may bedetermined by checking whether or not a DC position exists for theposition of the last non-zero coefficient in the above-described manner.

iii. In the case of the ISP mode and the single tree type, the i or iimethod may be applied. That is, in the case of the ISP mode and when thenumber i is applied to the single tree type, it is possible to omit thechecking of the position of the last non-zero coefficient for both theluma block and the chroma block and allow LFNST index signaling.Alternatively, by applying section ii, for the partition blocks for theluma component, the checking of the position of the last non-zerocoefficient is omitted, and for the partition blocks for the chromacomponent (if ISP is not applied for the chroma component, the number ofpartition blocks can be considered as 1), the position of the lastnon-zero coefficient is checked in the above-described manner, therebydetermining whether or not to signal the LFNST index.

E. When it is confirmed that the transform coefficient exists at aposition other than a position where the LFNST transform coefficient mayexist even for one partition block among all partition blocks, the LFNSTindex signaling may be omitted.

For example, in the case of a 4×4 partition block and an 8×8 partitionblock, LFNST transform coefficients may exist at eight positions fromthe DC position according to the transform coefficient scanning order inthe VVC standard, and the remaining positions are filled with zeros.Additionally, if it is equal to or greater than 4×4 and is not a 4×4partition block nor an 8×8 partition block, LFNST transform coefficientsmay exist at 16 positions from the DC position according to thetransform coefficient scanning order in the VVC standard, and all theremaining positions are filled with zeros.

Accordingly, if the non-zero transform coefficients exists in the regionwhich should be filled with the zero value after progressing theresidual coding, the LFNST index signaling may be omitted.

Meanwhile, in the case of the ISP mode, the length condition isindependently viewed for the horizontal direction and the verticaldirection, and DST-7 is applied instead of DCT-2 without signaling forthe MTS index. It is determined whether or not the horizontal orvertical length is greater than or equal to 4 and less than or equal to16, and a primary transform kernel is determined according to thedetermination result. Accordingly, in the case of the ISP mode, when theLFNST can be applied, the following transform combination configurationis possible.

When the LFNST index is 0 (including the case in which the LFNST indexis inferred as 0), the primary transform decision condition at the timeof the ISP included in the current VVC standard may be followed. Inother words, it may be checked whether or not the length condition(being equal to or greater than 4 or equal to or less than 16) isindependently satisfied for the horizontal and vertical directions,respectively, and if it is satisfied, DST-7 may be applied instead ofDCT-2 for primary transform, while, if it is not satisfied, DCT-2 may beapplied.

2. For a case in which the LFNST index is greater than 0, the followingtwo configurations may be possible as a primary transform.

A. DCT-2 can be applied to both horizontal and vertical directions.

B. The primary transform decision condition at the time of the ISPincluded in the current VVC standard may be followed. In other words, itmay be checked whether or not the length condition (being equal to orgreater than 4 or equal to or less than 16) is independently satisfiedfor the horizontal and vertical directions, respectively, and if it issatisfied, DST-7 may be applied instead of DCT-2, while, if it is notsatisfied, DCT-2 may be applied.

In the ISP mode, image information may be configured such that the LFNSTindex is transmitted for each partition block rather than for eachcoding unit. In this case, in the above-described LFNST index signalingmethod, it may be regarded that only one partition block exists in aunit in which the LFNST index is transmitted, and it may be determinedwhether or not to signal the LFNST index.

Meanwhile, the signaling order of the LFNST index and the MTS index willbe described below.

According to an example, the LFNST index signaled in residual coding maybe coded after the coding position for the last non-zero coefficientposition, and the MTS index may be coded immediately after the LFNSTindex. In the case of this configuration, the LFNST index may besignaled for each transform unit. Alternatively, even if not signaled inresidual coding, the LFNST index may be coded after the coding for thelast significant coefficient position, and the MTS index may be codedafter the LFNST index.

The syntax of residual coding according to an example is as follows.

TABLE 4 residual_coding( x0, y0, log2TbWidth, log2TbHeight, cIdx ) { if( ( sps_mts_enabled_flag && cu_sbt_flag && log2TbWidth < 6 &&log2TbHeight < 6 )       && cIdx = = 0 && log2TbWidth > 4 )  log2ZoTbWidth = 4  else   log2ZoTbWidth = Min( log2TbWidth, 5 ) MaxCcbs = 2 * ( 1 << log2TbWidth ) * ( 1<< log2TbHeight )  if( (sps_mts_enabled_flag && cu_sbt_flag && log2TbWidth < 6 && log2TbHeight <6 )       && cIdx = = 0 && log2TbHeight > 4 )   log2ZoTbHeight = 4  else  log2ZoTbHeight = Min( log2TbHeight, 5 )  if( log2TbWidth > 0 )  last_sig_coeff_x_prefix  if( log2TbHeight > 0 )  last_sig_coeff_y_prefix  if( last_sig_coeff_x_prefix > 3 )  last_sig_coeff_x_suffix  if( last_sig_coeff_y_prefix > 3 )  last_sig_coeff_y_suffix  remBinsPass1 = ( ( 1 << ( log2TbWidth +log2TbHeight ) ) * 7 ) >> 2  log2SbW = ( Min( log2TbWidth, log2TbHeight) < 2 ? 1 : 2 )  log2SbH = log2SbW  if( log2TbWidth + log2TbHeight > 3 ){    if( log2TbWidth < 2 ) {      log2SbW = log2TbWidth    log2SbH = 4 −log2sbW   } else if( log2TbHeight < 2 ) {    log2SbH = log2TbHeight   log2SbW = 4 − log2SbH   }  }  numSbCoeff = 1 << ( log2SbW + log2SbH ) lastScanPos = numSbCoeff  lastSubBlock = ( 1 << ( log2TbWidth +log2TbHeight − ( log2SbW +  log2SbH ) ) ) − 1  do {    if( lastScanPos == 0 ) {    lastScanPos = numSbCoeff    lastSubBlock- -   }  lastScanPos- -   xS = DiagScanOrder[ log2TbWidth − log2SbW ][log2TbHeight −   log2SbH ]         [ lastSubBlock ][ 0 ]   yS =DiagScanOrder[ log2TbWidth − log2SbW ][ log2TbHeight −   log2SbH ]        [ lastSubBlock ][ 1 ]   xC = ( xS << log2SbW ) + DiagScanOrder[log2SbW ][ log2SbH ][   lastScanPos ][ 0 ]   yC = ( yS << log2SbH ) +DiagScanOrder[ log2SbW ][ log2SbH ][   lastScanPos ][ 1 ]  } while( ( xC!= LastSignificantCoeffX ) | | ( yC !=  LastSignificantCoeffY ) )  cbWidth = CbWidth[ 0 ][ x0 ][ y0 ]   cbHeight = CbHeight[ 0 ][ x0 ][y0 ]  if( Min( log2TbWidth, log2TbHeight ) >= 2 && sps_lfnst_enabled_flag = = 1 &&   CuPredMode[ chType ][ x0 ][ y0 ] = =MODE_INTRA &&   IntraSubPartitionsSplit[ x0 ][ y0 ] = = ISP_NO_SPLIT &&  ( !intra_mip_flag[ x0 ][ y0 ] | | Min( log2TbWidth, log2TbHeight  ) >= 4 ) &&   Max( cbWidth, cbHeight ) <= MaxTbSizeY &&     ( cIdx = =0 | | ( treeType = = DUAL_TREE_CHROMA &&     ( cIdx = = 1 | | tu_cbf_cb[x0 ][ y0 ] == 0 ) ) ) ) {   if( lastSubBlock = = 0 && lastScanPos > 0 &&       !( lastScanPos > 7 && ( log2TbWidth = = 2 | |        log2TbWidth= = 3 )        && log2TbWidth = = log2TbHeight ) )    lfnst_idx[ x0 ][y0 ]  }  if( cIdx = = 0 && lfnst_idx[ x0 ][ y0 ] = = 0 &&   (log2TbWidth <= 5 ) && (log2TbHeight <= 5 ) &&   ( LastSignificantCoeffX< 16 ) && ( LastSignificantCoeffY < 16 )   &&   (IntraSubPartitionsSplit[ x0 ][ y0 ] = = ISP_NO_SPLIT ) && (  !cu_sbt_flag ) ) {   if( ( ( CuPredMode[ chType ][ x0 ][ y0 ] = =MODE_INTER &&    sps_explicit_mts_inter_enabled_flag )    | | (CuPredMode[ chType ][ x0 ][ y0 ] = = MODE_INTRA &&   sps_explicit_mts_intra_enabled_flag ) ) )    tu_mts_idx[ x0 ][ y0 ] }  if( tu_mts_idx[ x0 ][ y0 ] > 0 && cIdx = = 0 && log2TbWidth > 4 )  log2ZoTbWidth = 4  if( tu_mts_idx[ x0 ][ y0 ] > 0 && cIdx = = 0 &&log2TbHeight > 4 )   log2ZoTbHeight = 4  log2TbWidth = log2ZoTbWidth log2TbHeight = log2ZoTbHeight   ...

The meanings of the major variables shown in Table 4 are as follows.

1. cbWidth, cbHeight: the width and height of the current coding block

2. log 2TbWidth, log 2TbHeight: the log value of base-2 for the widthand height of the current transform block, it may be reduced, byreflecting the zero-out, to a top-left region in which a non-zerocoefficient may exist.

sps_lfnst_enabled_flag: a flag indicating whether or not the LFNST isenabled, if the flag value is 0, it indicates that the LFNST is notenabled, and if the flag value is 1, it indicates that the LFNST isenabled. It is defined in the sequence parameter set (SPS).

4. CuPredMode[chType][x0][y0]: a prediction mode corresponding to thevariable chType and the (x0, y0) position, chType may have values of 0and 1, wherein 0 indicates a luma component and 1 indicates a chromacomponent. The (x0, y0) position indicates a position on the picture,and MODE_INTRA (intra prediction) and MODE_INTER (inter prediction) arepossible as a value of CuPredModel[chType][x0][y0].

5. IntraSubPartitionsSplit[x0][y0]: the contents of the (x0, y0)position are the same as in No. 4. It indicates which ISP partition atthe (x0, y0) position is applied, ISP_NO_SPLIT indicates that the codingunit corresponding to the (x0, y0) position is not divided intopartition blocks.

6. intra_mip_flag[x0][y0]: the contents of the (x0, y0) position are thesame as in No. 4 above. The intra_mip_flag is a flag indicating whetheror not a matrix-based intra prediction (MIP) prediction mode is applied.If the flag value is 0, it indicates that MIP is not enabled, and if theflag value is 1, it indicates that MIP is enabled.

7. cIdx: the value of 0 indicates luma, and the values of 1 and 2indicate Cb and Cr which are respectively chroma components.

8. treeType: indicates single-tree and dual-tree, etc. (SINGLE_TREE:single tree, DUAL_TREE_LUMA: dual tree for luma component,DUAL_TREE_CHROMA: dual tree for chroma component)

9. tu_cbf_cb[x0][y0]: the contents of the (x0, y0) position are the sameas in No. 4. It indicates the coded block flag (CBF) for the Cbcomponent. If its value is 0, it means that no non-zero coefficients arepresent in the corresponding transform unit for the Cb component, and ifits value is 1, it indicates that non-zero coefficients are present inthe corresponding transform unit for the Cb component.

10. lastSubBlock: It indicates a position in the scan order of asub-block (Coefficient Group (CG)) in which the last non-zerocoefficient is located. 0 indicates a sub-block in which the DCcomponent is included, and in the case of being greater than 0, it isnot a sub-block in which the DC component is included.

11. lastScanPos: It indicates the position where the last significantcoefficient is in the scan order within one sub-block. If one sub-blockincludes 16 positions, values from 0 to 15 are possible.

12. lfnst_idx[x0][y0]: LFNST index syntax element to be parsed. If it isnot parsed, it is inferred as a value of 0. That is, the default valueis set to 0, indicating that LFNST is not applied.

13. LastSignificantCoeffX, LastSignificantCoeffY: They indicate the xand y coordinates where the last significant coefficient is located inthe transform block. The x-coordinate starts at 0 and increases fromleft to right, and the y-coordinate starts at 0 and increases from topto bottom. If the values of both variables are 0, it means that the lastsignificant coefficient is located at DC.

14. cu_sbt_flag: A flag indicating whether or not SubBlock Transform(SBT) included in the current VVC standard is enabled. If a flag valueis 0, it indicates that SBT is not enabled, and if the flag value is 1,it indicates that SBT is enabled.

15. sps_explicit_mts_inter_enabled_flag,sps_explicit_mts_intra_enabled_flag: Flags indicating whether or notexplicit MTS is applied to inter CU and intra CU, respectively. If acorresponding flag value is 0, it indicates that MTS is not enabled toan inter CU or an intra CU, and if the corresponding flag value is 1, itindicates that MTS is enabled.

16. tu_mts_idx[x0][y0]: MTS index syntax element to be parsed. If it isnot parsed, it is inferred as a value of 0. That is, the default valueis set to 0, indicating that DCT-2 is enabled to both the horizontal andvertical directions.

As shown in Table 4, in the case of a single tree, it is possible todetermine whether or not to signal the LFNST index using only the lastsignificant coefficient position condition for luma. That is, if theposition of the last significant coefficient is not DC and the lastsignificant coefficient exists in the top-left sub-block (CG), forexample, a 4×4 block, then the LFNST index is signaled. In this case, inthe case of the 4×4 transform block and the 8×8 transform block, theLFNST index is signaled only when the last significant coefficientexists at positions 0 to 7 in the top-left sub-block.

In the case of the dual tree, the LFNST index is signaled independentlyof each of luma and chroma, and in the case of chroma, the LFNST indexcan be signaled by applying the last significant coefficient positioncondition only to the Cb component. The corresponding condition may notbe checked for the Cr component, and if the CBF value for Cb is 0, theLFNST index may be signaled by applying the last significant coefficientposition condition to the Cr component.

‘Min(log 2TbWidth, log 2TbHeight)>=2’ of Table 4 may be expressed as“Min(tbWidth, tbHeight)>=4”, and ‘Min(log 2TbWidth, log 2TbHeight)>=4’may be expressed as “Min(tbWidth, tbHeight)>=16”.

In Table 4, log 2ZoTbWidth and log 2ZoTbHeight mean log values whosewidth and height base are 2 (base-2) for the top-left region where thelast significant coefficient may exist by zero-out, respectively.

As shown in Table 4, log 2ZoTbWidth and log 2ZoTbHeight values may beupdated in two places. The first is before the MTS index or LFNST indexvalue is parsed, and the second is after the MTS index is parsed.

The first update is before the MTS index (tu_mts_idx[x0][y0]) value isparsed, so log 2ZoTbWidth and log 2ZoTbHeight can be set regardless ofthe MTS index value.

After the MTS index is parsed, log 2ZoTbWidth and log 2ZoTbHeigh are setfor an MTS index of greater than 0 (DST-7/DCT-8 combination). WhenDST-7/DCT-8 is independently applied in each of the horizontal andvertical directions in the primary transform, there may be up to 16significant coefficients per row or column in each direction. That is,after applying DST-7/DCT-8 with a length of 32 or greater, up to 16transform coefficients may be derived for each row or column from theleft or top. Accordingly, in a 2D block, when DST-7/DCT-8 is applied inboth the horizontal direction and the vertical direction, significantcoefficients may exist in an only up to 16×16 top-left region.

In addition, when DCT-2 is independently applied in each of thehorizontal and vertical directions in the current primary transform,there may be up to 32 significant coefficients per row or column in eachdirection. That is, when applying DCT-2 with a length of 64 or greater,up to 32 transform coefficients may be derived for each row or columnfrom the left or top. Accordingly, in a 2D block, when DCT-2 is appliedin both the horizontal direction and the vertical direction, significantcoefficients may exist in an only up to 32×32 top-left region.

In addition, when DST-7/DCT-8 is applied on one side, and DCT-2 isapplied on the other side to horizontal and vertical directions, 16significant coefficients may exist in the former direction, and 32significant coefficients may exist in the latter direction. For example,in the case of a 64×8 transform block, if DCT-2 is applied in thehorizontal direction and DST-7 is applied in the vertical direction (itmay occur in a situation where implicit MTS is applied), a significantcoefficient may exist in up to a top-left 32×8 region.

If, as shown in Table 4, log 2ZoTbWidth and log 2ZoTbHeight are updatedin two places, that is, before MTS index parsing, the ranges oflast_sig_coeffx_prefix and last_sig_coeff_y_prefix may be determined bylog 2ZoTbWidth and log 2ZoTbHeight as shown in the table below.

TABLE 5 7.4.9.11 Residual coding semantics ......last_sig_coeff_x_prefix specifies the prefix of the column position ofthe last significant coefficient in scanning order within a transformblock. The values of last_sig_coeff_x_prefix shall be in the range of 0to ( log2ZoTbWidth << 1 ) − 1, inclusive. When last_sig_coeff_x_prefixis not present, it is inferred to be 0. last_sig_coeff_y_prefixspecifies the prefix of the row position of the last significantcoefficient in scanning order within a transform block. The values oflast_sig_coeff_y_prefix shall be in the range of 0 to ( log2ZoTbHeight<< 1 ) − 1, inclusive. When last_sig_coeff_y_prefix is not present, itis inferred to be 0. ......

Additionally, in this case, the maximum values oflast_sig_coeff_x_prefix and last_sig_coeff_y_prefix may be set byreflecting log 2ZoTbWidth and log 2TbHeight values in the binarizationprocess for last_sig_coeff_x_prefix and last_sig_coeff_y_prefix.

TABLE 6 Table 9-77 - Syntax elements and associated binarizationsresidual coding last_sig_coeff_x_prefix TR cMax = ( log2ZoTbWidth << 1 )− 1, ( ) cRiceParam = 0 last_sig_coeff_y_prefix TR cMax = (log2ZoTbHeight << 1 ) −1, cRiceParam = 0 last_sig_coeff_x_suffix FL cMax= ( 1 << ( ( last_sig_coeff_x_prefix >> 1 ) − 1 ) − 1 )last_sig_coeff_y_suffix FL cMax = ( 1 << ( ( last_sig_coeff_y_prefix >>1 ) − 1 ) − 1 ) ...... ...... ......

According to an example, in a case where the ISP mode and the LFNST isapplied, when signaling of Table 4 is applied, specification text may beconfigured as shown in Table 7. Compared with Table 4, the condition ofsignaling the LFNST index only in a case excluding the ISP mode(intraSubPartitionsSplit[x0][y0]==ISP_NO_SPLIT in Table 4) is deleted.

In a single tree, when an LFNST index transmitted for aluma component(cIdx=0) is reused for a chroma component, an LFNST index transmittedfor a first ISP partition block in which a significant coefficientexists may be applied to a chroma transform block. Alternatively, evenin a single tree, an LFNST index may be signaled for a chroma componentseparately from that for a luma component. Description of variables inTable 7 is the same as in Table 4.

TABLE 7 residual_coding( x0, y0, log2TbWidth, log2TbHeight, cIdx ) { ...  if( log2TbWidth > 0 )   last_sig_coeff_x_prefix  if(log2TbHeight > 0 )   last_sig_coeff_y_prefix  if(last_sig_coeff_x_prefix > 3 )   last_sig_coeff_x_suffix  if(last_sig_coeff_y_prefix > 3 )   last_sig_coeff_y_suffix  ...   cbWidth =CbWidth[ 0 ][ x0 ][ y0 ]   cbHeight = CbHeight[ 0 ][ x0 ][ y0 ]   if(Min( log2TbWidth, log2TbHeight ) >= 2 &&   sps_lfnst_enabled_flag = = 1&&    CuPredMode[ chType ][ x0 ][ y0 ] = = MODE_INTRA &&    (!intra_mip_flag[ x0 ][ y0 ] | | Min( log2TbWidth, log2TbHeight    ) >= 4) &&    Max( cbWidth, cbHeight ) <= MaxTbSizeY &&    ( cIdx = = 0 | | (treeType = = DUAL_TREE_CHROMA &&    ( cIdx = = 1 | | tu_cbf_cb[ x0 ][ y0] == 0 ) ) ) ) {    if( lastSubBlock = = 0 && lastScanPos > 0 &&     !(lastScanPos > 7 && ( log2TbWidth = = 2 | |     log2TbWidth = = 3 )     && log2TbWidth = = log2TbHeight ) )     lfnst_idx[ x0 ][ y0 ]   }  if( cIdx = = 0 && lfnst_idx[ x0 ][ y0 ] = = 0 &&    ( log2TbWidth <= 5) && ( log2TbHeight <= 5 ) &&    ( LastSignificantCoeffX < 16 ) && (LastSignificantCoeffY < 16 )    &&    ( IntraSubPartitionsSplit[ x0 ][y0 ] = = ISP_NO_SPLIT ) && (    !cu_sbt_flag ) ) {    if( ( (CuPredMode[ chType ][ x0 ][ y0 ] = = MODE_INTER &&    sps_explicit_mts_inter_enabled_flag )     | | ( CuPredMode[ chType][ x0 ][ y0 ] = =     MODE_INTRA &&    sps_explicit_mts_intra_enabled_flag ) ) )     tu_mts_idx[ x0 ][ y0 ]  }

According to an example, the LFNST index and/or the MTS index may besignaled in a coding unit level. As described above, the LFNST index mayhave three values of 0, 1, and 2, where 0 indicates that the LFNST isnot applied, and 1 and 2 respectively indicate a first candidate and asecond candidate of two LFNST kernel candidates included in a selectedLFNST set. The LFNST index is coded through truncated unarybinarization, and the values of 0, 1, and 2 may be coded as bin stringsof 0, 10, and 11, respectively.

According to an example, the LFNST may be applied only when DCT-2 isapplied in both the horizontal direction and the vertical direction inthe primary transform. Therefore, if the MTS index is signaled aftersignaling the LFNST index, the MTS index may be signaled only when theLFNST index is 0, and primary transform may be performed by applyingDCT-2 in both the horizontal direction and the vertical directionwithout signaling the MTS index when the LFNST index is not 0.

The MTS index may have values of 0, 1, 2, 3, and 4, where 0, 1, 2, 3,and 4 may indicate that DCT-2/DCT-2, DST-7/DST-7, DCT-8/DST-7, DST-7,DCT-8, DCT-8/DCT-8 are applied in the horizontal and verticaldirections, respectively. In addition, the MTS index may be codedthrough truncated unitary binarization, and the values of 0, 1, 2, 3,and 4 may be coded as bin strings of 0, 10, 110, 1110, and 1111,respectively.

The LFNST index and the MTS index may be signaled at the coding unitlevel, and the MITS index may be sequentially coded after the LFNSTindex at the coding unit level. The coding unit syntax table for this isas follows.

TABLE 8 Descriptor coding_unit( x0, y0, cbWidth, CbHeight, cqtDepth,treeType, modeType ) {  ...... ae(v)  if( cu_cbf ) {   ......  LfnstDcOnly = 1   LfnstZeroOutSigCoeffFlag = 1   transform_tree( x0,y0, cbWidth, cbHeight, treeType )   lfnstWidth = ( treeType = =DUAL_TREE_CHROMA ) ? cbWidth / SubWidthC      : (IntraSubPartitionsSplitType = = ISP_VER_SPLIT) ? cbWidth /NumIntraSubPartitions : cbWidth   lfnstHeight = ( treeType = =DUAL_TREE_CHROMA ) ? cbHeight / SubHeightC      : (IntraSubPartitionsSplitType = = ISP_HOR_SPLIT) ? cbHeight /NumIntraSubPartitions : cbHeight   if( Min( lfnstWidth, lfnstHeight ) >=4 &&   sps_lfnst_enabled_flag = = 1 &&    CuPredMode[ chType ][ x0 ][ y0] = =    MODE_INTRA &&    ( !intra_mip_flag[ x0 ][ y0 ] | | Min(lfnstWidth,    lfnstHeight ) >= 16 ) &&    !transform_skip_flag[ x0 ][y0 ] && Max( cbWidth,    cbHeight ) <= MaxTbSizeY) {    if( (IntraSubPartitionsSplitType ! =    ISP_NO_SPLIT | | LfnstDcOnly = = 0 )&& LfnstZeroOutSigCoeffFlag = = 1 )     lfnst_idx[ x0 ][ y0 ] ae(v)   }  if( tu_cbf_luma[ x0 ][ y0 ] && treeType !=   DUAL_TREE_CHROMA &&    lfnst_idx[ x0 ][ y0 ] = = 0 && ( cbWidth <= 32 )     && ( cbHeight<= 32 )     &&     ( IntraSubPartitionsSplit[ x0 ][ y0 ] = =    ISP_NO_SPLIT )     && ( !cu_sbt_flag ) ) {    if( ( ( CuPredMode[chType ][ x0 ][ y0 ] = =    MODE_INTER &&    sps_explicit_mts_inter_enabled_flag )     | | ( CuPredMode[ chType][ x0 ][ y0 ] = =     MODE_INTRA &&    sps_explicit_mts_intra_enabled_flag ) ) )     tu_mts_idx[ x0 ][ y0 ]ae(v)   }  }

The variable LfnistDcOnly and the variable LfnistZeroOutSigCoeffFlag ofTable 8 may be set as shown in Table 9 below.

The variable LfnstDcOnly is equal to 1 when all last significantcoefficients are located at DC positions (top-left positions) fortransform blocks having a coded block flag (CBF, equal to 0 if there isat least one significant coefficient in a corresponding block, and isequal to 0 otherwise) of 1, and is equal to 0 otherwise. Specifically,in a case of dual tree luma, the position of the last significantcoefficient is checked with respect to one luma transform block, and ina case of dual tree chroma, the position of the last significantcoefficient is checked with respect to both a transform block for Cb anda transform block for Cr. In a case of a single tree, the position ofthe last significant coefficient may be checked with respect totransform block for luma, Cb, and Cr.

The variable LfnstZeroOutSigCoeffFlag is equal to 0 if there is asignificant coefficient at a zero-out position when the LFNST isapplied, and is equal to 1 otherwise.

lfnst_idx[x0][y0] included in Table 8 and subsequent tables indicates anLFNST index for a corresponding coding unit, and tu_mts_idx[x0][y0]indicates an MTS index for the corresponding coding unit.

As shown in Table 8, the condition for signaling lfnst_idx[x0][y0] mayinclude a condition for checking whether the transform_skip_flag[x0][y0]value is 0 (!transform_skip_flag[x0][y0]). In this case, the conditionfor checking whether the existing tu_mts_idx[x0][y0] value is 0 (thatis, checking whether DCT-2 in both the horizontal and verticaldirections) may be omitted.

transform_skip_flag[x0][y0] indicates whether the coding unit is codedin the transform skip mode in which a transform is skipped, and the flagis signaled before the MTS index and the LFNST index. That is, sincelfnst_idx[x0][y0] is signaled before the value of tu_mtx_idx[x0][y0] issignaled, only the condition for the value oftransform_skip_flag[x0][y0] may be be checked.

As shown in Table 8, a plurality of conditions is checked when codingtu_mts_idx[x0][y0], and tu_mts_idx[x0][y0] is signaled only when thevalue of ifnst_idx[x0][y0] is 0 as described above.

tu_cbf_luma[x0][y0] is a flag indicating whether a significantcoefficient exists for a luma component, and cbWidth and cbHeightindicate the width and height of the coding unit for the luma component,respectively.

According to Table 8, when both the width and the height of the codingunit for the luma component are 32 or less, tu_mts_idx[x0][y0] issignaled, that is, whether an MTS is applied is determined by the widthand height of the coding unit for the luma component.

According to another example, when transform block (TU) tiling occurs(e.g., when a maximum transform size is set to 32, a 64×64 coding unitis divided into four 32×32 transform blocks and coded), the MTS indexmay be signaled based on the size of each transform block. For example,when both the width and the height of a transform block are 32 or less,the same MTS index value may be applied to all transform blocks in acoding unit, thereby applying the same primary transform. In addition,when transform block tiling occurs, the value of tu_cbf_luma[x0][y0] inTable 8 may be a CBF value for a top-left transform block, or may be setto 1 when a CBF value for even one transform block of all transformblocks is 1.

As shown in Table 8, even in the ISP mode, (IntraSubPartitionsSplitType!=ISP_NO_SPLIT) lfnst_idx[x0][y0] may be configured to be signaled, andthe same LFNST index value may be applied to all ISP partition blocks.

Meanwhile, tu_mts_idx[x0][y0] may be signaled only in a mode excludingthe ISP mode (IntraSubPartitionsSplit[x0][y0]==ISP_NO_SPLIT).

As shown in Table 8, when the MTS index is signaled immediately afterthe LFNST index, information on the primary transform cannot be knownwhen performing residual coding. That is, the MTS index is signaledafter residual coding. Accordingly, in a residual coding part, a part onwhich a zero-out is performed while leaving only 16 coefficients forDST-7 or DCT-8 having a length of 32 may be changed as shown below inTable 9.

TABLE 9 Descriptor residual_coding( x0, y0, log2TbWidth, log2TbHeight,cIdx ) {  if( ( sps_mts_enabled_flag && cu_sbt_flag &&  log2TbWidth < 6&& log2TbHeight < 6 )  && cIdx = = 0 && log2TbWidth > 4 )  log2ZoTbWidth = 4  else   log2ZoTbWidth = Min( log2TbWidth, 5 ) MaxCcbs = 2 * ( 1 << log2TbWidth ) * ( 1<<  log2TbHeight )  if( (sps_mts_enabled_flag && cu_sbt_flag &&  log2TbWidth < 6 && log2TbHeight< 6 )   && cIdx = = 0 && log2TbHeight > 4 )   log2ZoTbHeight = 4  else  log2ZoTbHeight = Min( log2TbHeight, 5 )  if( log2TbWidth > 0 )  last_sig_coeff_x_prefix ae(v)  if( log2TbHeight > 0 )  last_sig_coeff_y_prefix ae(v)  if( last_sig_coeff_x_prefix > 3 )  last_sig_coeff_x_suffix ae(v)  if( last_sig_coeff_y_prefix > 3 )  last_sig_coeff_y_suffix ae(v)  log2TbWidth = log2ZoTbWidth log2TbHeight = log2ZoTbHeight  remBinsPass1 = ( ( 1 << ( log2TbWidth + log2TbHeight ) ) * 7 ) >> 2  log2SbW = ( Min( log2TbWidth, log2TbHeight ) < 2 ? 1 : 2 )  log2SbH = log2SbW  if( log2TbWidth + log2TbHeight > 3) {   if( log2TbWidth < 2 ) {    log2SbW = log2TbWidth    log2SbH = 4 −log2SbW   } else if( log2TbHeight < 2 ) {    log2SbH = log2TbHeight   log2SbW = 4 − log2SbH   }  }  numSbCoeff = 1 << ( log2SbW + log2SbH ) lastScanPos = numSbCoeff  lastSubBlock = ( 1 << ( log2TbWidth +log2TbHeight − (  log2SbW + log2SbH ) ) ) − 1  do {   if( lastScanPos == 0 ) {    lastScanPos = numSbCoeff    lastSubBlock- -   }  lastScanPos- -   xS = DiagScanOrder[ log2TbWidth − log2SbW ][  log2TbHeight − log2SbH ]     [ lastSubBlock ][ 0 ]   yS =DiagScanOrder[ log2TbWidth − log2SbW ][   log2TbHeight − log2SbH ]     [lastSubBlock ][ 1 ]   xC = ( xS << log2SbW ) + DiagScanOrder[ log2SbW ][  log2SbH ][ lastScanPos ][ 0 ]   yC = ( yS << log2SbH ) +DiagScanOrder[ log2SbW ][   log2SbH ][ lastScanPos ][ 1 ]  } while( ( xC!= LastSignificantCoeffX ) | | ( yC != LastSignificantCoeffY ) )  if(lastSubBlock = = 0 &&log2TbWidth >= 2 &&  log2TbHeight >= 2 &&  !transform_skip_flag[ x0 ][ y0 ] && lastScanPos > 0 )   LfnstDcOnly= 0 if( ( lastSubBlock > 0 && log2TbWidth >= 2  &&log2TbHeight >= 2 ) | |  ( lastScanPos > 7 && ( log2TbWidth = = 2 | |   log2TbWidth = = 3 ) &&  log2TbWidth = = log2TbHeight ) )   LfnstZeroOutSigCoeffFlag = 0

As shown in Table 9, in a process of determining log 2ZoTbWidth and log2ZoTbHeight (where log 2ZoTbWidth and log 2ZoThHeight respectivelydenote the base-2 log values of the width and height of atop-left regionremaining after the zero-out is performed), checking the value oftu_mts_idx[x0][y0] may be omitted.

Binarization of last_sig_coeff_x_prefix and last_Sig_coeff_y_prefix inTable 9 may be determined based on log 2ZoThWidth and log 2ZoThHeight asshown in Table 6.

Further, as shown in Table 9, a condition of checkingsps_mts_enable_flag may be added when determining log 2ZoTbWidth and log2ZoTbHeight in residual coding.

According to an example, when information on the position of the lastsignificant coefficient of the luma transform block is recorded in theresidual coding process, the MTS index may be signaled as shown in Table10.

TABLE 10 Descriptor coding_unit( x0, y0, cbWidth, cbHeight, cqtDepth,treeType, modeType ) {   ...... ae(v)  if( cu_cbf ) {   ......  LfnstDcOnly = 1   LfnstZeroOutSigCoeffFlag = 1    LumaLastSignificantCoeffX = 0     LumaLastSignificantCoeffY = 0  transform_tree( x0, y0, cbWidth, cbHeight, treeType )   lfnstWidth = (treeType = = DUAL_TREE_CHROMA   ) ? cbWidth / SubWidthC      : (IntraSubPartitionsSplitType = = ISP_VER_SPLIT) ? cbWidth /NumIntraSubPartitions : cbWidth   lfnstHeight = ( treeType = =DUAL_TREE_CHROMA    ) ? cbHeight / SubHeightC      : (IntraSubPartitionsSplitType = = ISP_HOR_SPLIT) ? cbHeight /NumIntraSubPartitions : cbHeight   if( Min( lfnstWidth, lfnstHeight ) >=4 &&   sps_lfnst_enabled_flag = = 1 &&    CuPredMode[ chType ][ x0 ][ y0] = =    MODE_INTRA &&    ( !intra_mip_flag[ x0 ][ y0 ] | | Min(lfnstWidth,    lfnstHeight ) >= 16 ) &&    !transform_skip_flag[ x0 ][y0 ] && Max( cbWidth,    cbHeight ) <= MaxTbSizeY) {    if( (IntraSubPartitionsSplitType ! =    ISP_NO_SPLIT | | LfnstDcOnly = = 0 )&& LfnstZeroOutSigCoeffFlag = = 1 )     lfnst_idx[ x0 ][ y0 ] ae(v)   }  if( tu_cbf_luma[ x0 ][ y0 ] && treeType !=   DUAL_TREE_CHROMA &&   lfnst_idx[ x0 ][ y0 ] = = 0 && ( cbWidth <= 32 ) &&    ( cbHeight <=32 ) &&    ( LumaLastSignificantCoeffX < 16 ) && (   LumaLastSignificantCoeffY < 16 ) &&    ( IntraSubPartitionsSplit[ x0][ y0 ] = =    ISP_NO_SPLIT ) && ( !cu_sbt_flag ) ) {    if( ( (CuPredMode[ chType ][ x0 ][ y0 ] = =    MODE_INTER &&    sps_explicit_mts_inter_enabled_flag )     | | ( CuPredMode[ chType][ x0 ][ y0 ] = =     MODE_INTRA &&    sps_explicit_mts_intra_enabled_flag ) ) )     tu_mts_idx[ x0 ][ y0 ]ae(v)   }  }

In Table 10, LumaLastSignificantCoeffX and LumaLastSignificantCoeffYindicate the X coordinate and Y coordinate of the last significantcoefficient position for the luma transformation block, respectively. Acondition that both LumaLastSignificantCoeffX andLumaLastSignificantCoeffY must be less than 16 is added to Table 10.When either of them is 16 or greater, DCT-2 is applied in both thehorizontal and vertical directions, it can be inferred that signalingfor tu_mts_idx x0 [y0] is omitted and DCT-2 is applied to both thehorizontal direction and the vertical direction.

When both LumaLastSignificantCoeffX and LumaLastSignificantCoeffY areless than 16, it means that the last significant coefficient exists inthe top-left 16×16 region. In the current VVC standard when DST-7 orDCT-8 of length 32 is applied, it indicates that there is a possibilitythat zero-out, which leaves only 16 transform coefficients from the leftor top, has been applied. Accordingly, it is possible to specify thetransform kernel used for the primary transformation by signalingtu_mts_idx[x0][y0].

Meanwhile, according to another example, the coding unit syntax table,the transform unit syntax table, and the residual coding syntax tableare as follows. According to Table 11, the MTS index moves from thetransform unit level to the coding unit level syntax, and is signaledafter LFNST index signaling. In addition, the constraint that does notallow LFNST when the ISP is applied to the coding unit has been removed.When the ISP is applied to the coding unit, the constraint that does notallow the LFNST is removed, so that the LFNST can be applied to allintra prediction blocks. In addition, both the MTS index and the LFNSTindex are conditionally signaled in the last part of the coding unitlevel.

TABLE 11 coding_unit( x0, y0, cbWidth, cbHeight, cqtDepth, treeType,modeType ) { . . .  LfnstDcOnly = 1  LfnstZeroOutSigCoeffFlag = 1 MtsZeroOutSigCoeffFlag = 1  transform_tree( x0, y0, cbWidth, cbHeight,treeType )  lfnstWidth = ( treeType = = DUAL_TREE_CHROMA ) ? cbWidth / SubWidthC     : ( IntraSubPartitionsSplitType = = ISP_VER_SPLIT) ?cbWidth / NumIntraSubPartitions : cbWidth  lfnstHeight = ( treeType = =DUAL_TREE_CHROMA ) ? cbHeight /  SubHeightC     : (IntraSubPartitionsSplitType = = ISP_HOR_SPLIT) ? cbHeight /NumIntraSubPartitions : cbHeight  if( Min( lfnstWidth, lfnstHeight ) >=4 &&  sps_lfnst_enabled_flag = = 1 &&   CuPredMode[ chType ][ x0 ][ y0 ]= = MODE_INTRA &&   ( !intra_mip_flag[ x0 ][ y0 ] | | Min( lfnstWidth,lfnstHeight   ) >= 16 ) &&  Max( cbWidth, cbHeight ) <= MaxTbSizeY) {  if( ( IntraSubPartitionsSplitType ! = ISP_NO_SPLIT | |   LfnstDcOnly == 0 ) && LfnstZeroOutSigCoeffFlag = = 1 )    lfnst_idx[ x0 ][ y0 ]  } if( treeType != DUAL_TREE_CHROMA && lfnst_idx[ x0 ][ y0   ] = = 0 &&  transform_skip_flag[ x0 ][ y0 ] = = 0 && Max( cbWidth, cbHeight   ) <=32 &&   IntraSubPartitionsSplit[ x0][ y0 ] = = ISP_NO_SPLIT && (  !cu_sbt_flag ) &&   MtsZeroOutSigCoeffFlag = = 1 && tu_cbf_luma[ x0 ][y0 ] ) {   if( ( ( CuPredMode[ chType ][ x0 ][ y0 ] = = MODE_INTER &&   sps_explicit_mts_inter_enabled_flag )    | | ( CuPredMode[ chType ][x0 ][ y0 ] = = MODE_INTRA &&    sps_explicit_mts_intra_enabled_flag ) ))    mts_idx[ x0 ][ y0 ]  } ...

TABLE 12 transform_unit( x0, y0, tbWidth, tbHeight, treeType,subTuIndex, chType ) { ...  if( tu_cbf_luma[ x0 ][ y0 ] && treeType != DUAL_TREE_CHROMA    && ( tbWidth <= 32 ) && ( tbHeight <= 32 )    && (IntraSubPartitionsSplit[ x0 ][ y0 ] = = ISP_NO_SPLIT     ) && (!cu_sbt_flag ) ) {   if( sps_transform_skip_enabled_flag && !BdpcmFlag[x0 ][ y0    ] &&     tbWidth <= MaxTsSize && tbHeight <= MaxTsSize )    transform_skip_flag[ x0 ][ y0 ]  } ...

TABLE 13 residual_coding( x0, y0, log2TbWidth, log2TbHeight, cIdx ) {...  if ( ( cu_sbt_flag && log2TbWidth < 6 && log2TbHeight < 6 )    &&cIdx = = 0 && log2TbWidth > 4 )   log2ZoTbWidth = 4  else  log2ZoTbWidth = Min( log2TbWidth, 5 )  MaxCcbs = 2 * ( 1 <<log2TbWidth ) * ( 1<< log2TbHeight )  if ( ( cu_sbt_flag && log2TbWidth< 6 && log2TbHeight < 6 )    && cIdx = = 0 && log2TbHeight > 4 )  log2ZoTbHeight = 4  else   log2ZoTbHeight = Min( log2TbHeight, 5 ) ... if( ( lastSubBlock > 0 && log2TbWidth >= 2 && log2TbHeight >=  2 ) | |  ( lastScanPos > 7 && ( log2TbWidth = = 2 | | log2TbWidth = = 3 )   &&  log2TbWidth = = log2TbHeight ) )   LfnstZeroOutSigCoeffFlag = 0  if( (LastSignificantCoeffX > 15 | | LastSignificantCoeffY > 15 ) &&  cIdx = =0 )   MtsZeroOutSigCoeffFlag = 0 ...

In Table 11. MtsZeroOutSigCoeffFlag is initially set to 1, and thisvalue may be changed in residual coding in Table 13. The value of avariable MtsZeroOutSigCoeffFlag is changed from 1 to 0 when asignificant coefficient exists in a region(LastSignificantCoeffX>15∥LastSignificantCoeffY>15) to be filled with 0sby a zero-out, in which case the MTS index is not signaled as shown inTable 11.

Meanwhile, as shown in Table 11, when tu_cbf_luma[x0][y0] is 0,mts_idx[x0][y0] coding may be omitted. That is, when the CBF value ofthe luma component is 0, since the transform is not applied, there is noneed to signal the MTS index, and thus the MTS index coding may beomitted.

According to an example, the above technical feature may be implementedin another conditional syntax. For example, after the MTS is performed,a variable indicating whether a significant coefficient exists in aregion other than the DC region of the current block may be derived, andwhen the variable indicates that the significant coefficient exists inthe region excluding the DC region, the MTS index can be signaled. Thatis, the existence of the significant coefficient in the region otherthan the DC region of the current block indicates that the value oftu_cbf_luma[x0][y0] is 1, and in this case, the MTS index can besignaled.

The variable may be expressed as MtsDcOnly, and after the variableMtsDcOnly is initially set to 1 at the coding unit level, the value ischanged to 0 when it is determined that the significant coefficient ispresent in the region except for the DC region of the current block inthe residual coding level. When the variable MtsDcOnly is 0, imageinformation may be configured such that the MTS index is signaled.

When tu_cbf_luma[x0][y0] is 0, since the residual coding syntax is notcalled at the transform unit level of Table 12, the initial value of 1of the variable MtsDcOnly is maintained. In this case, since thevariable MtsDcOnly is not changed to 0, the image information may beconfigured so that the MTS index is not signaled. That is, the MTS indexis not parsed and signaled.

Meanwhile, the decoding apparatus may determine the color index cIdx ofthe transform coefficient to derive the variable MtsZeroOutSigCoeffFlagof Table 13. The color index cIdx of 0 means a luma component.

According to an example, since the MTS can be applied only to the lumacomponent of the current block, the decoding apparatus can determinewhether the color index is luma when deriving the variableMtsZeroOutSigCoeffFlag for determining whether to parse the MTS index.

The variable MtsZeroOutSigCoeffFlag is a variable indicating whether thezero-out is performed when the MTS is applied. It indicates whether thetransform coefficient exists in the top-left region where the lastsignificant coefficient may exist due to the zero-out after the MTS isperformed, that is, in the region other than the top-left 16×16 region.The variable MtsZeroOutSigCoeffFlag is initially set to 1 at the codingunit level as shown in Table 11 (MtsZeroOutSigCoeffFlag=1), and when thetransform coefficient exists in the region other than the 16×16 region,its value can be changed from 1 to 0 in the residual coding level asshown in Table 13 (MtsZeroOutSigCoeffFlag=0). When the value of thevariable MtsZeroOutSigCoeffFlag is 0, the MTS index is not signaled.

As shown in Table 13, at the residual coding level, a non-zero-outregion in which a non-zero transform coefficient may exist may be setdepending on whether or not the zero-out accompanying the MTS isperformed, and even in this case, the color index (cIdx) is 0, thenon-zero-out region may be set to the top-left 16×16 region of thecurrent block.

As such, when deriving the variable that determines whether the MTSindex is parsed, it is determined whether the color component is luma orchroma. However, since LFNST can be applied to both the luma componentand the chroma component of the current block, the color component isnot determined when deriving a variable for determining whether to parsethe LFNST index.

For example. Table 11 shows a variable LfnstZeroOutSigCoeffFlag that mayindicate that zero-out is performed when LFNST is applied. The variableLfnstZeroOutSigCoeffFlag indicates whether a significant coefficientexists in the second region except for the first region at the top-leftof the current block. This value is initially set to 1, and when thesignificant coefficient is present in the second region, the value canbe changed to 0. The LFNST index can be parsed only when the value ofthe initially set variable LfnstZeroOutSigCoeffFlag is maintained at 1.When determining and deriving whether the variableLfnstZeroOutSigCoeffFlag value is 1, since the LFNST may be applied toboth the luma component and the chroma component of the current block,the color index of the current block is not determined.

FIG. 15 illustrates a CCLM applicable when deriving an intra predictionmode for a chroma block according to an embodiment.

In this specification, a “reference sample template” may refer to a setof neighboring reference samples of a current chroma block forpredicting the current chroma block. A reference sample template may bepredefined, and information on the reference sample template may besignaled from the encoding apparatus 200 to the decoding apparatus 300.

Referring to FIG. 15 , a set of samples shaded in a single line adjacentto a 4×4 block, which is a current chroma block, refers to a referencesample template. The reference sample template is configured in a singleline of reference samples, while a reference sample region in a lumaregion corresponding to the reference sample template is configured intwo lines as shown in FIG. 15 .

In an embodiment, when intra encoding of a chroma image is performed ina Joint Exploration Test Model (JEM) used in the Joint Video ExplorationTeam (JVET), a cross-component linear model (CCLM) may be used. The CCLMis a method of predicting a pixel value of a chroma image from a pixelvalue of a reconstructed luma image, and is based on a high correlationbetween a luma image and a chroma image.

CCLM prediction of Cb and Cr chroma images may be performed based on thefollowing equation.

Pred_(C)(i,j)=α·Rec′ _(L)(i,j)+β  [Equation 11]

Here, Pred_(c) (i,j) denotes a Cb or Cr chroma image to be predicted,Rec_(L)′(i,j) denotes a reconstructed luminance image adjusted to achroma block size, and (i, j) denotes the coordinates of a pixel. In a4:2:0 color format, since the size of a luminance image is twice that ofa chroma image, Rec_(L)′ with the chroma block size needs to begenerated through downsampling, and therefore the chroma imagePredc(i,j), pixels of the luminance image to be used for the chromaimage pred_(c)(i,j) may be employed considering both Rec_(L)(2i, 2j) andneighboring pixels. Rec_(L)′(i,j) may be referred to as a down-sampledluma sample.

For example, Rec_(L)′(i,j) may be derived using six neighboring pixelsas shown in the following equation.

Rec′ _(L)(x,y)=(2×Rec _(L)(2x,2y)+2×Rec _(L)(2x,2y+1)+Rec_(L)(2x−1.2y)+Rec _(L)(2x+L2y)+Rec _(L)(2x−1.2y+1)+Rec_(L)(2x+1.2y+1)+4)>>3  [Equation 12]

α and β denote a cross-correlation and an average difference between aneighboring template of the Cb or Cr chroma block and a neighboringtemplate of the luminance block in the shaded region in FIG. 15 . Forexample, α and β are represented by Equation 13.

$\begin{matrix}{{\alpha = \frac{{N \cdot {\sum\left( {{L(n)} \cdot {C(n)}} \right)}} - {\sum{{L(n)} \cdot {\sum{C(n)}}}}}{{N \cdot {\sum\left( {{L(n)} \cdot {L(n)}} \right)}} - {\sum{{L(n)} \cdot {\sum{L(n)}}}}}}{\beta = \frac{{\sum{C(n)}} - {\alpha \cdot {\sum{L(n)}}}}{N}}} & \left\lbrack {{Equation}13} \right\rbrack\end{matrix}$

L(n) denotes neighboring reference samples and/or left neighboringsamples of a luma block corresponding to a current chroma image. C(n)denotes neighboring reference samples and/or left neighboring samples ofthe current chroma block to which encoding is currently applied, and(i,j) denotes a pixel position. In addition, L(n) may denotedown-sampled upper neighboring samples and/or left neighboring samplesof the current luma block. N may denote the total number of pixel pair(luminance and chroma) values used for calculation of a CCLM parameter,and may indicate a value that is twice a smaller value of the width andthe height of the current chroma block.

Pictures may be divided into a sequence of coding tree units (CTUs). ACTU may correspond to a coding tree block (CTB). Alternatively, the CTUmay include a coding tree block of luma samples and a coding tree blockof corresponding chroma samples. A tree type may be classified as asingle tree (SINGLE_TREE) or a dual tree (DUAL_TREE) according towhether a luma block and a corresponding chroma block have an individualpartition structure. A single tree may indicate that the chroma blockhas the same partition structure as the luma block, and a dual tree mayindicate that the chroma component block has a partition structuredifferent from that of the luma) block.

When an LFNST is applied to a chroma transform block according to anexample, it is necessary to refer to information on a collocated lumatransform block.

Existing specification text about a relevant part is shown in thefollowing table.

TABLE 14 8.7.4 Transformation process for scaled transform coefficients8.7.4.1 General Inputs to this process are: - a luma location ( xTbY,yTbY ) specifying the top-left sample of the current luma transformblock relative to the top-left luma sample of the current picture, - avariable nTbW specifying the width of the current transform block, - avariable nTbH specifying the height of the current transform block, - avariable cIdx specifying the colour component of the current block, an(nTbW)x(nTbH) array d[ x ][ y ] of scaled transform coefficients with x= 0..nTbW − 1, y = 0..nTbH − 1 ... When lfnst_idx is not equal to 0 andboth nTbW and nTbH are greater than or equal to 4, the followingapplies: ... - When predModeIntra is equal to either INTRA _(—) LT _(—)CCLM, INTRA _(—) L _(—) CCLM, or INTRA _(—) T _(—) CCLM, predModeIntrais derived as follows: - If intra _(—) mip _(—) flag[ xTbY + nTbW / 2 ][yTbY + nTbH / 2 ] is equal to 1, predModeIntra is set equal to INTRA_(—) PLANAR. - Otherwise, if CuPredMode[ 0 ][ xTbY + nTbW / 2 ][ yTbY +nTbH / 2 ] is equal to MODE _(—) IBC or MODE _(—) PLT, predModeIntra isset equal to INTRA _(—) DC. - Otherwise, predModeIntra is set equal toIntraPredModeY[ xTbY + nTbW / 2 ][ yTbY + nTbH / 2 ].

As shown in Table 14, when a current intra prediction mode is a CCLMmode, the value of a variable predModeIntra for the chroma transformblock is determined by taking an intra prediction mode value for theco-located luma transform block (part indicated in italics). The intraprediction mode value (predModelntra value) of the luma transform blockmay be subsequently used to determine an LFNST set.

However, variables nTbW and nTbH input as input values of this transformprocess denote the width and height of the current transform block.Thus, when the current block is a luma transform block, the variablesnTbW and nTbH may denote the width and height of the luma transformblock, and when the current block is a chroma transform block, thevariables nTbW and nTbH denote the width and height of the chromatransform block.

Here, the variables nTbW and nTbH in the italic part of Table 14 denotethe width and height of the chroma transform block that do not reflectthe color format and thus do not accurately indicate a referenceposition of the luma transform block corresponding to the chromatransform block. Therefore, the italic part of Table 14 may be modifiedas shown in the following table.

TABLE 15 - When predModeIntra is equal to either INTRA_LT_CCLM,INTRA_L_CCLM, or INTRA_T_CCLM, predModeIntra is derived as follows: - Ifintra_mip_flag[ xTbY + ( nTbW * SubWidthC ) / 2 ][ yTbY + ( nTbH *SubHeightC ) / 2 ] is equal to 1, predModeIntra is set equal toINTRA_PLANAR. - Otherwise, if CuPredMode[ 0 ][ xTbY + ( nTbW * SubWidthC) / 2 ][yTbY + ( nTbH * SubHeightC ) / 2 ] is equal to MODE_IBC orMODE_PLT, predModeIntra is set equal to INTRA_DC. - Otherwise,predModeIntra is set equal to IntraPredModeY[ xTbY + ( nTbW * SubWidthC) / 2 ][ yTbY + ( nTbH * SubHeightC ) / 2 ]-

As shown in Table 15, nTbW and nTbH are changed to (nTbW*SubWidthC)/2and (nTbH*SubHeightC)/2, respectively. xTbY and yTbY may denote a lumaposition in the current picture (the top-left sample of the current lumatransform block relative to the top-left luma sample of the currentpicture), and nTbW and nTbH may denote the width and height of thetransform block currently coded (a variable nTbW specifying the width ofthe current transform block, and a variable nTbH specifying the heightof the current transform block).

When the currently coded transform block is a chroma (Cb or Cr)transform block, nTbW and nTbH are the width and height of the chromatransform block, respectively. Accordingly, when the currently codedtransform block is a chroma transform block (cIdx>0), a referenceposition for a collocated luma transform block needs to be obtainedusing the width and height of the luma transform block when obtainingthe reference position. In Table 15, SubWidthC and SubHeightC are valuesset according to the color format (e.g., 4:2:0, 4:2:2, or 4:4:4), andspecifically, a width ratio and a height ratio between a luma componentand a chroma component, respectively (see Table below). Thus, in a caseof the chroma transform block, (nTbW*SubWidthC) and (nTbH*SubHeightC)may be the width and height with respect to the collocated lumatransform block, respectively.

Consequently, xTbY+(nTbW*SubWidthC)/2 and yTbY+(nTbH*SubHeightC)/2denote the value of a center position in the collocated luma transformblock based on a top-left position of the current picture and can thusprecisely indicate the collocated luma transform block.

TABLE 16 Chroma format SubWidthC SubHeightC Monochrome 1 1 4:2:0 2 24:2:2 2 1 4:4:4 1 1 4:4:4 1 1

In Table 15, a variable predModeIntra denotes an intra prediction modevalue, and the value of the variable predModelntra equal toINTRA_LT_CCLM, INTRA_L_CCLM, or INTRA_T_CCLM indicates that the currenttransform block is a chroma transform block. According to an example, inthe current VVC standard, INTRA_LT_CCLM, INTRA_L_CCLM, and INTRA_T_CCLMrespectively correspond to mode values of 81, 82, and 83 among intraprediction mode values. Therefore, as shown in Table 15, the referenceposition for the collocated luma transform block needs to be obtainedusing the value of xTbY+(nTbW*SubWidthC)/2 and the value ofyTbY+(nTbH*SubHeightC)/2.

As shown in Table 15, the value of the variable predModeIntra is updatedin view of both a variableintra_mip_flag[xTbY+(nTbW*SubWidthC)/2][yTbY+(nTbH*SubHeightC)/2] and avariableCuPredMode[0][xTbY+(nTbW*SubWidthC)/2][yTbY+(nTbH*SubHeightC)/2].

intra_mip_flag is a variable indicating whether the current transformblock (or coding unit) is coded by a matrix-based intra prediction (MIP)method, and intra_mip_flag[x][y] is a flag value indicating whether MIPis applied to a position corresponding to coordinates (x,y) based on theluma component when a top-left position in the current picture isdefined as (0, 0). The x and y coordinates increase from left to rightand from top to bottom, respectively, and when the flag indicatingwhether the MIP is applied is 1, the flag indicates that the MIP isapplied. When the flag indicating whether the MIP is applied is 0, theflag indicates that the MIP is not applied. The MIP may be applied onlyto the luma block.

According to the modified part of Table 15, when the value ofintra_mip_flag[xTbY+(nTbW*SubWidthC)/2][yTbY+(nTbH*SubHeightC)/2] in thecollocated luma transform block is 1, the value of predModelntra is setto a planar mode (INTRA_PLANAR).

The value of the variableCuPredMode[0][xTbY+(nTbW*SubWidthC)/2][yTbY+(nTbH*SubHeightC)/2] denotesa prediction mode value corresponding to corrdicates(xTbY+(nTbW*SubWidthC)/2, yTbY+(nTbH*SubHeightC)/2) when the top-leftposition of the current picture for the luma component is defined (0,0). The prediction mode value may have MODE_INTRA, MODE_IBC, MODE_PLT,and MODE_INTER values, which denote an intra prediction mode, an intrablock copy (IBC) prediction mode, a palette (PLT) coding mode, and aninter prediction mode, respectively. According to Table 15, when thevalue of the variable CuPredMode[0][xTbY+(nTbWSubWidthC)/2][yTbY+(nTbH*SubHeightC)/2] is MODE_IBC or MODE_PLT thevalue of the variable predModeIntra is set to a DC mode. In a case otherthan the two cases, the value of the variable predModeIntra is set toIntraPredModeY[xTbY+(nTbW*SubWidthC)/2][yTbY+(nTbH*SubHeightC)/2] (intraprediction mode value corresponding to a center position in thecollocated luma transform block).

According to an example, the value of the variable predModelntra may beupdated once more based on the predModelntra value updated in Table 15considering whether wide-angle intra prediction is performed as shown inthe following table.

TABLE 17 8.4.5.2.6 Wide angle intra prediction mode mapping processInputs to this process are: - a variable predModeIntra specifying theintra prediction mode, - a variable nTbW specifying the transform blockwidth, - a variable nTbH specifying the transform block height, - avariable cIdx specifying the colour component of the current block.Output of this process is the modified intra prediction modepredModeIntra. The variables nW and nH are derived as follows: - IfIntraSubPartitionsSplitType is equal to ISP_NO_SPLIT or cIdx is notequal to 0, the following applies:  nW = nTbW (8-111)  nH = nTbH(8-112) - Otherwise ( IntraSubPartitionsSplitType is not equal toISP_NO_SPLIT and cIdx is equal to 0 ), the following applies:  nW = nCbW(8-113)  nH = nCbH (8-114) The variable whRatio is set equal to Abs(Log2( nW / nH ) ). For non-square blocks (nW is not equal to nH), theintra prediction mode predModeIntra is modified as follows: - If all ofthe following conditions are true, predModeIntra is set equal to (predModeIntra + 65 ). - nW is greater than nH - predModeIntra is greaterthan or equal to 2 - predModeIntra is less than ( whRatio > 1 ) ? ( 8 +2 * whRatio ) : 8 - Otherwise, if all of the following conditions aretrue, predModeIntra is set equal to ( predModeIntra − 67 ). - nH isgreater than nW - predModeIntra is less than or equal to 66 -predModeIntra is greater than ( whRatio > 1 ) ? ( 60 − 2 * whRatio ) :60

Input values of predModeintra, nTbW, and nTbH in a mapping process shownin Table 17 are the same as the value of the variable predModelntraupdated in Table 15 and nTbW and nTbH referenced in Table 15,respectively.

In Table 17, nCbW and nCbH denote the width and height of a coding blockcorresponding to the transform block, respectively, and a variableIntraSubPartitionsSplitType denotes whether the ISP mode is applied,wherein IntraSubPartitionsSplitType equal to ISP_NO_SPLIT indicates thatthe coding unit is not partitioned by the ISP (i.e., the ISP mode is notapplied). The variable IntraSubPartitionsSplitType not equal toISP_NO_SPLIT indicates that the ISP mode is applied and thus the codingunit is partitioned into two or four partition blocks. In Table 17, cIdxis an index indicating a color component. A cIdx value equal to 0denotes a luma block, and a cIdx value not equal to 0 indicates a chromablock. The predModelntra value output through the mapping process ofTable 17 is a value updated in consideration of whether a wide-angleintra prediction (WAIP) mode is applied.

With respect to the predModeIntra value updated through Table 17, anLFNST set may be determined through a mapping relationship shown in thefollowing table.

TABLE 18 predModeIntra lfnstTrSetIdx predModeIntra < 0 1 0 <=predModeIntra <= 1 0  2 <= predModeIntra <= 12 1 13 <= predModeIntra <=23 2 24 <= predModeIntra <= 44 3 45 <= predModeIntra <= 55 2 56 <=predModeIntra <= 80 1

In the above table, lfnstTrSetIdx denotes an index indicating an LFNSTset and has a value from 0 to 3, which indicates that a total of fourLFNST sets are configured. Each LFNST set may include two transformkernels, that is, LFNST kernels (the transform kernels may be 16×16matrices or 16×48 matrices based on a forward direction depending on aregion to which an LFNST is applied), and a transform kernel to beapplied among the two transform kernels may be specified throughsignaling of the LFNST index. In addition, it is possible to specifywhether to apply the LFNST through the LFNST index. In the current VVCstandard, the LFNST index may have values of 0, 1, and 2, 0 indicatesthat no LFNST is applied, and 1 and 2 indicate the two transformkernels, respectively.

The following drawings are provided to describe specific examples of thepresent disclosure. Since the specific designations of devices or thedesignations of specific signals/messages/fields illustrated in thedrawings are provided for illustration, technical features of thepresent disclosure are not limited to specific designations used in thefollowing drawings.

FIG. 16 is a flowchart illustrating an operation of a video decodingapparatus according to an embodiment of the present disclosure.

Each process disclosed in FIG. 16 is based on some of details describedwith reference to FIG. 4 to FIG. 15 . Therefore, a description ofspecific details overlapping the details described with reference toFIG. 3 to FIG. 15 will be omitted or will be schematically made.

The decoding apparatus 300 according to an embodiment may obtain intraprediction mode information and an LFNST index from a bitstream (S1610).

The intra prediction mode information may include an intra predictionmode for a neighboring block (e.g., a left and/or upper neighboringblock) of a current block and an most probable mode (MPM) indexindicating one of MPM candidates in an MPM list derived based onadditional candidate modes or remaining intra prediction modeinformation indicating one of remaining intra prediction modes notincluded in the MPM candidates.

In addition, the intra mode information may include flag informationsps_cclm_enabled_flag indicating whether a CCLM is applied to thecurrent block and information intra_chroma_pred_mode about an intraprediction mode for a chroma component.

LFNST index information is received as syntax information, and thesyntax information is received as a binarized bin string including 0 and1.

A syntax element of the LFNST index according to the present embodimentmay indicate whether an inverse LFNST or an inverse non-separabletransform is applied and any one of transform kernel matrices includedin a transform set, and when the transform set includes two transformkernel matrices, the syntax element of the transform index may havethree values.

That is, according to an embodiment, the values of the syntax element ofthe LFNST index may include 0 indicating that no inverse LFNST isapplied to a target block, 1 indicating a first transform kernel matrixamong the transform kernel matrices, and 2 indicating a second transformkernel matrix among the transform kernel matrices.

The decoding apparatus 300 may decode information on quantized transformcoefficients for the current block from the bitstream, and may derivequantized transform coefficients for the target block based on theinformation on the quantized transform coefficients for the currentblock. Information on the quantized transform coefficients for thetarget block may be included in a sequence parameter set (SPS) or aslice header and may include at least one of information on whether anRST is applied, information on a reduced factor, information on aminimum transform size for applying an RST, information on a maximumtransform size for applying an RST, an inverse RST size, and informationon a transform index indicating any one of transform kernel matricesincluded in a transform set.

The decoding apparatus 300 may derive transform coefficients bydequantizing residual information on the current block, that is, thequantized transform coefficients, and may arrange the derived transformcoefficients in a predetermined scanning order.

Specifically, the derived transform coefficients may be arranged in 4×4block units according to a reverse diagonal scan order, and transformcoefficients in a 4×4 block may also be arranged according to thereverse diagonal scan order. That is, the dequantized transformcoefficients may be arranged according to a reverse scan order appliedin a video codec, such as in VVC or HEVC.

The transform coefficient derived based on the residual information maybe the dequantized transform coefficient as described above, or may bequantized transform coefficients. That is, the transform coefficientsmay be any data for checking whether there is non-zero data in thecurrent block regardless of quantization.

The decoding apparatus may derive an intra prediction mode for a chromablock as a CCLM mode based on the intra prediction mode information(S1620).

For example, the decoding apparatus may receive information on the intraprediction mode for the current chroma block through the bitstream, andmay derive the CCLM mode as the intra prediction mode for the currentchroma block based on the intra prediction mode information.

The CCLM mode may include a top-left CCLM mode, a top CCLM mode, or aleft CCLM mode.

As described above, the decoding apparatus may derive a residual sampleby applying an LFNST, which is a non-separable transform, or an MTS,which is a separable transform, and these transforms may be performedrespectively based on the LFNST index indicating an LFNST kernel, thatis, an LFNST matrix, and an MTS index indicating an MTS kernel.

For the LFNST, an LFNST set needs to be determined, and the LFNST sethas a mapping relationship with an intra prediction mode for the currentblock.

The decoding apparatus may update the intra prediction mode for thechroma block based on an intra prediction mode for a luma blockcorresponding to the chroma block for inverse LFNST of the chroma block(S1630).

According to an example, the updated intra prediction mode may bederived as an intra prediction mode corresponding to a specific positionin the luma block, and the specific position may be set based on a colorformat of the chroma block.

The specific position may be a center position of the luma block and maybe represented by ((xTbY+(nTbW*SubWidthC)/2),(yTbY+(nTbH*SubHeightC)/2)).

In the center position, xTbY and yTbY denote top-left coordinates of theluma block, that is, a top-left position in a luma sample reference fora current transform block, nTbW and nTbH denote the width and height ofthe chroma block, and SubWidthC and SubHeightC correspond to variablescorresponding to the color format. ((xTbY+(nTbW*SubWidthC)/2),(yTbY+(nTbH*SubHeightC)/2)) denotes a center position of a lumatransform block, andIntraPredModeY[xTbY+(nTbW*SubWidthC)/2][yTbY+(nTbH*SubHeightC)/2]denotes an intra prediction mode for the luma block for the position.

SubWidthC and SubHeightC may be derived as shown in Table 16. That is,when the color format is 4:2:0, SubWidthC and SubHeighC are 2, and whenthe color format is 4:2:2, SubWidthC is 2 and SubHeightC is 1.

As shown in Table 15, to designate the specific position of the lumablock corresponding to the chroma block regardless of the color format,the color format is reflected in a variable indicating the specificposition.

According to an example, when the intra prediction mode for the lumablock corresponding to the specific position is a matrix-based intraprediction (hereinafter, “MIP”) mode, the decoding apparatus may set theupdated intra prediction mode to an intra planar mode.

The MIP mode may be referred to as affine linear weighted intraprediction (ALWIP) or matrix weighted intra prediction (MWIP). When MIPis applied to the current block, prediction samples for the currentblock may be derived ii) by performing a matrix-vector multiplicationprocedure i) using neighboring reference samples which have beensubjected to an averaging procedure and iii) by further performing ahorizontal/vertical interpolation procedure.

Alternatively, according to an example, when the intra prediction modecorresponding to the specific position is an intra block copy (IBC) modeor a palette mode, the decoding apparatus may set the updated intraprediction mode to an intra DC mode.

The IBC prediction mode or the palette mode may be used for coding acontent image/video including a game, for example, screen content coding(SCC). The IBC basically performs prediction within a current picturebut may be performed similarly to inter prediction in that a referenceblock is derived within the current picture. That is, the IBC may use atleast one of inter prediction techniques described in the presentdisclosure. The palette mode may be considered as an example of intracoding or intra prediction. When the palette mode is applied, a value ofa sample in the picture may be signaled based on information on apalette table and a palette index.

In summary, when the intra prediction mode for the center position isthe MIP mode, the IBC mode, and the palette mode, the intra predictionmode for the chroma block may be updated to a specific mode, such as theintra planar mode or the intra DC mode.

When the intra prediction mode for the center position is not the MIPmode, the IBC mode, and the palette mode, the intra prediction mode forthe chroma block may be updated to the intra prediction mode of the lumablock with respect to the center position in order to reflect anassociation between the chroma block and the luma block.

When the chroma block is not a square, the decoding apparatus may remapthe updated intra prediction mode to the wide-angle intra predictionmode (S1640).

In order to determine the LFNST set, the intra prediction mode may beremapped, that is, updated or modified by reflecting the wide-angleintra mode as shown in Table 17.

The input values of predModelntra, nTbW, and nTbH of the mapping processpresented in Table 17 are the values of predModeIntra updated in Table15 and nTbW and nTbH corresponding to the width and height of the chromablock referenced in Table 15, respectively.

The variable whRatio representing the ratio of the width and height ofthe block may be set to Abs(Log 2(nW/nH)). Alternatively, it may beexpressed as Abs(Log 2(nW)−Log 2(nH)).

For example, when the width of the chroma block is greater than theheight, the updated intra mode is 2 or more, and the updated intra modeis a variable (whRatio >1)?(8+2*whRatio):8 [where whRatio is Abs(Log2(nW/nH)))], the updated intra mode may be remapped to “updated intramode+65”.

In this document, “x?y:z” operator indicates that if x is TRUE, then xbecomes y, and if x is otherwise, x equals z (if x is TRUE, evaluates tothe value of y; otherwise, evaluates to the value of z).

Or, when the height of the chroma block is greater than the width, theupdated intra mode is 66 or less, and the updated intra mode is avariable (whRatio >1)?(60−2*whRatio):60 [where whRatio is Abs(Log2(nW/nH))], the updated intra mode may be remapped to “updated intramode−67”.

That is, the decoding apparatus may re-update the intra prediction modefor determining the LFNST set by reflecting the non-square of the chromablock.

The decoding apparatus may determine an LFNST set including LFNSTmatrices based on the remapped intra prediction mode (S1650), and mayderive transform coefficients for the chroma block based on an LFNSTmatrix derived from the LFNST set (S1660).

Any one of the plurality of LFNST matrices may be selected based on theLFNST set and the LFNST index.

As shown in Table 18, the LFNST transform set is derived according tothe intra prediction mode, and 81 to 83 indicating the CCLM mode in theintra prediction mode are omitted, because the LFNST transform set isderived using an intra mode value for a corresponding luma block or theremapped wide-angle intra-mode values in the CCLM mode.

According to an example, as shown in Table 18, any one of the four LFNSTsets may be determined according to the intra prediction mode for thecurrent block, and an LFNST set to be applied to the current chromablock may also be determined.

The decoding apparatus may perform an inverse RST, for example, aninverse LFNST, by applying the LFNST matrix to the dequantized transformcoefficients, thereby deriving modified transform coefficients for thecurrent chroma block.

The decoding apparatus may derive residual samples from the transformcoefficients through a primary inverse transform (S1670). An MTS may beused in the primary inverse transform.

In addition, the decoding apparatus may generate reconstructed samplesbased on residual samples for the current block and prediction samplesfor the current block. The current block may be the current luma blockor the current chroma block.

The following drawings are provided to describe specific examples of thepresent disclosure. Since the specific designations of devices or thedesignations of specific signals/messages/fields illustrated in thedrawings are provided for illustration, technical features of thepresent disclosure are not limited to specific designations used in thefollowing drawings.

FIG. 17 is a flowchart illustrating an operation of a video encodingapparatus according to an embodiment of the present disclosure.

Each process disclosed in FIG. 17 is based on some of details describedwith reference to FIG. 4 to FIG. 15 . Therefore, a description ofspecific details overlapping the details described with reference toFIG. 2 and FIG. 4 to FIG. 15 will be omitted or will be schematicallymade.

The encoding apparatus 200 according to an embodiment may derive anintra prediction mode for a chroma block as a CCLM mode (S1710).

For example, the encoding apparatus may determine the intra predictionmode for the current chroma block based on a rate-distortion (RD) cost(or RDO). Here, the RD cost may be derived based on the sum of absolutedifferences (SAD). The encoding apparatus may determine the CCLM mode asthe intra prediction mode for the current chroma block based on the RDcost.

The CCLM mode may include a top-left CCLM mode, a top CCLM mode, or aleft CCLM mode.

The encoding apparatus may encode information on the intra predictionmode for the current chroma block, and the information on the intraprediction mode may be signaled through a bitstream. Prediction-relatedinformation on the current chroma block may include the information onthe intra prediction mode.

The encoding apparatus may derive prediction samples for the chromablock based on the CCLM mode (S1720).

According to an embodiment, the encoding apparatus may derive residualsamples for the chroma block based on the prediction samples (S1730).

According to an embodiment, the encoding apparatus may derive transformcoefficients for the chroma block based on a primary transform on theresidual samples.

The primary transform may be performed through a plurality of transformkernels, in which case a transform kernel may be selected based on theintra prediction mode.

The encoding apparatus may update the intra prediction mode for thechroma block based on an intra prediction mode for a luma blockcorresponding to the chroma block for LFNST of the chroma block (S1740).

As shown in Table 15, the encoding apparatus may update the CCLM modefor the chroma block based on the intra prediction mode for the lumablock corresponding to the chroma block (−When predModelntra is equal toeither INTRA_LT_CCLM, INTRA_L_CCLM, or INTRA_T_CCLM, predModeintra isderived as follow).

According to an example, the updated intra prediction mode may bederived as an intra prediction mode corresponding to a specific positionin the luma block, and the specific position may be set based on a colorformat of the chroma block.

The specific position may be a center position of the luma block and maybe represented by ((xTbY+(nTbW*SubWidthC)/2),(yTbY+(nTbH*SubHeightC)/2)).

In the center position, xTbY and yTbY denote top-left coordinates of theluma block, that is, a top-left position in a luma sample reference fora current transform block, nTbW and nTbH denote the width and height ofthe chroma block, and SubWidthC and SubHeightC correspond to variablescorresponding to the color format. ((xTbY+(nTbW*SubWidthC)/2),(yTbY+(nTbH*SubHeightC)/2)) denotes a center position of a lumatransform block, andIntraPredModeY[xTbY+(nTbW*SubWidthC)/2][yTbY+(nTbH*SubHeightC)/2]denotes an intra prediction mode for the luma block for the position.

SubWidthC and SubHeightC may be derived as shown in Table 16. That is,when the color format is 4:2:0, SubWidthC and SubHeightC are 2, and whenthe color format is 4:2:2, SubWidthC is 2 and SubHeightC is 1.

As shown in Table 15, to designate the specific position of the lumablock corresponding to the chroma block regardless of the color format,the color format is reflected in a variable indicating the specificposition.

According to an example, when the intra prediction mode for the lumablock corresponding to the specific position is a matrix-based intraprediction (hereinafter, “MIP”) mode, the encoding apparatus may set theupdated intra prediction mode to an intra planar mode.

The MIP mode may be referred to as affine linear weighted intraprediction (ALWIP) or matrix weighted intra prediction (MWIP). When MIPis applied to the current block, prediction samples for the currentblock may be derived ii) by performing a matrix-vector multiplicationprocedure i) using neighboring reference samples which have beensubjected to an averaging procedure and iii) by further performing ahorizontal/vertical interpolation procedure.

Alternatively, according to an example, when the intra prediction modecorresponding to the specific position is an intra block copy (IBC) modeor a palette mode, the encoding apparatus may set the updated intraprediction mode to an intra DC mode.

The IBC prediction mode or the palette mode may be used for coding acontent image/video including a game, for example, screen content coding(SCC). The IBC basically performs prediction within a current picturebut may be performed similarly to inter prediction in that a referenceblock is derived within the current picture. That is, the IBC may use atleast one of inter prediction techniques described in the presentdisclosure. The palette mode may be considered as an example of intracoding or intra prediction. When the palette mode is applied, a value ofa sample in the picture may be signaled based on information on apalette table and a palette index.

In summary, when the intra prediction mode for the center position isthe MIP mode, the IBC mode, and the palette mode, the intra predictionmode for the chroma block may be updated to a specific mode, such as theintra planar mode or the intra DC mode.

When the intra prediction mode for the center position is not the MIPmode, the IBC mode, and the palette mode, the intra prediction mode forthe chroma block may be updated to the intra prediction mode of the lumablock with respect to the center position in order to reflect anassociation between the chroma block and the luma block.

When the chroma block is not a square, the encoding apparatus may remapthe updated intra prediction mode to the wide-angle intra predictionmode (S1750).

In order to determine the LFNST set, the intra prediction mode may beremapped, that is, updated or modified by reflecting the wide-angleintra mode as shown in Table 17.

The input values of predModeintra, nTbW, and nTbH of the mapping processpresented in Table 17 are the values of predModelntra updated in Table15 and nTbW and nTbH corresponding to the width and height of the chromablock referenced in Table 15, respectively.

The variable whRatio representing the ratio of the width and height ofthe block may be set to Abs(Log 2(nW/nH)).

For example, when the width of the chroma block is greater than theheight, the updated intra mode is 2 or more, and the updated intra modeis a variable (whRatio >1)?(8+2*whRatio):8 [where whRatio is Abs(Log2(nW/nH))], the updated intra mode may be remapped to “updated intramode+65”.

Or, when the height of the chroma block is greater than the width, theupdated intra mode is 66 or less, and the updated intra mode is avariable (whRatio >1)?(60−2*whRatio):60 [where whRatio is Abs(Log2(nW/nH))], the updated intra mode may be remapped to “updated intramode−67”.

That is, the encoding apparatus may re-update the intra prediction modefor determining the LFNST set by reflecting the non-square of the chromablock.

The encoding apparatus may determine an LFNST set including LFNSTmatrices based on the remapped intra prediction mode (S1760), and mayderive modified transform coefficients for the chroma block based on theresidual samples and an LFNST matrix (S1770).

The encoding apparatus may determine the transform set based on amapping relationship according to the intra prediction mode applied tothe current block and may perform an LFNST, that is, a non-separabletransform, based on any one of two LFNST matrices included in thetransform set.

As described above, a plurality of transform sets may be determinedaccording to an intra prediction mode for a transform block to betransformed. A matrix applied to the LFNST is the transpose of a matrixused in an inverse LFNST

In one example, the LFNST matrix may be a non-square matrix in which thenumber of rows is smaller than the number of columns.

The encoding apparatus may derive quantized transform coefficients byperforming quantization based on the modified transform coefficients forthe current chroma block and may encode and output image informationincluding information on the quantized transform coefficients,information on the intra prediction mode, and an LFNST index indicatingthe LFNST matrix (S1780).

Specifically, the encoding apparatus 200 may generate the information onthe quantized transform coefficients and may encode the generatedinformation on the quantized transform coefficients.

In one example, the information on the quantized transform coefficientsmay include at least one of information on whether the LFNST is applied,information on a reduced factor, information on a minimum transform sizefor applying the LFNST, and information on a maximum transform size forapplying the LFNST.

The encoding apparatus may encode, as the information on the intra mode,flag information indicating whether the CCLM is applied to the currentblock, which is sps_cclm_enabled_flag, and information on an intraprediction mode for a chroma component, which is intra_chroma_pred_mode.

The information on the CCLM mode, which is intra_chroma_pred_mode, mayindicate the top-left CCLM mode, the top CCLM mode, or the left CCLMmode.

In the present disclosure, at least one of quantization/dequantizationand/or transform/inverse transform may be omitted. Whenquantization/dequantization is omitted, a quantized transformcoefficient may be referred to as a transform coefficient. Whentransform/inverse transform is omitted, the transform coefficient may bereferred to as a coefficient or a residual coefficient, or may still bereferred to as a transform coefficient for consistency of expression.

Further, in the present disclosure, a quantized transform coefficientand a transform coefficient may be referred to as a transformcoefficient and a scaled transform coefficient, respectively. In thiscase, residual information may include information on a transformcoefficient(s), and the information on the transform coefficient(s) maybe signaled through a residual coding syntax. Transform coefficients maybe derived based on the residual information (or information on thetransform coefficient(s)), and scaled transform coefficients may bederived through inverse transform (scaling) of the transformcoefficients. Residual samples may be derived based on the inversetransform (transform) of the scaled transform coefficients. Thesedetails may also be applied/expressed in other parts of the presentdisclosure.

In the above-described embodiments, the methods are explained on thebasis of flowcharts by means of a series of steps or blocks, but thepresent disclosure is not limited to the order of steps, and a certainstep may be performed in order or step different from that describedabove, or concurrently with another step. Further, it may be understoodby a person having ordinary skill in the art that the steps shown in aflowchart are not exclusive, and that another step may be incorporatedor one or more steps of the flowchart may be removed without affectingthe scope of the present disclosure.

The above-described methods according to the present disclosure may beimplemented as a software form, and an encoding apparatus and/ordecoding apparatus according to the disclosure may be included in adevice for image processing, such as, a TV, a computer, a smartphone, aset-top box, a display device or the like.

When embodiments in the present disclosure are embodied by software, theabove-described methods may be embodied as modules (processes, functionsor the like) to perform the above-described functions. The modules maybe stored in a memory and may be executed by a processor. The memory maybe inside or outside the processor and may be connected to the processorin various well-known manners. The processor may include anapplication-specific integrated circuit (ASIC), other chipset, logiccircuit, and/or a data processing device. The memory may include aread-only memory (ROM), a random access memory (RAM), a flash memory, amemory card, a storage medium, and/or other storage device. That is,embodiments described in the present disclosure may be embodied andperformed on a processor, a microprocessor, a controller or a chip. Forexample, function units shown in each drawing may be embodied andperformed on a computer, a processor, a microprocessor, a controller ora chip.

Further, the decoding apparatus and the encoding apparatus to which thepresent disclosure is applied, may be included in a multimediabroadcasting transceiver, a mobile communication terminal, a home cinemavideo device, a digital cinema video device, a surveillance camera, avideo chat device, a real time communication device such as videocommunication, a mobile streaming device, a storage medium, a camcorder,a video on demand (VoD) service providing device, an over the top (OTT)video device, an Internet streaming service providing device, athree-dimensional (3D) video device, a video telephony video device, anda medical video device, and may be used to process a video signal or adata signal. For example, the over the top (OTT) video device mayinclude a game console, a Blu-ray player, an Internet access TV, a Hometheater system, a smartphone, a Tablet PC, a digital video recorder(DVR) and the like.

In addition, the processing method to which the present disclosure isapplied, may be produced in the form of a program executed by acomputer, and be stored in a computer-readable recording medium.Multimedia data having a data structure according to the presentdisclosure may also be stored in a computer-readable recording medium.The computer-readable recording medium includes all kinds of storagedevices and distributed storage devices in which computer-readable dataare stored. The computer-readable recording medium may include, forexample, a Blu-ray Disc (BD), a universal serial bus (USB), a ROM, aPROM, an EPROM, an EEPROM, a RAM, a CD-ROM, a magnetic tape, a floppydisk, and an optical data storage device. Further, the computer-readablerecording medium includes media embodied in the form of a carrier wave(for example, transmission over the Internet). In addition, a bitstreamgenerated by the encoding method may be stored in a computer-readablerecording medium or transmitted through a wired or wirelesscommunication network. Additionally, the embodiments of the presentdisclosure may be embodied as a computer program product by programcodes, and the program codes may be executed on a computer by theembodiments of the present disclosure. The program codes may be storedon a computer-readable carrier.

Claims disclosed herein can be combined in a various way. For example,technical features of method claims of the present disclosure can becombined to be implemented or performed in an apparatus, and technicalfeatures of apparatus claims can be combined to be implemented orperformed in a method. Further, technical features of method claims andapparatus claims can be combined to be implemented or performed in anapparatus, and technical features of method claims and apparatus claimscan be combined to be implemented or performed in a method.

What is claimed is:
 1. An image decoding method performed by a decodingapparatus, the method comprising: obtaining intra prediction modeinformation and an LFNST index from a bitstream; deriving an intraprediction mode for a chroma block as a cross-component linear model(CCLM) mode based on the intra prediction mode information; derivesprediction samples for the chroma block based on the CCLM mode;performing an LFNST to derive transform coefficients; and derivingresidual samples for the chroma block based on the transformcoefficients, wherein the performing of the LFNST comprising: updatingthe intra prediction mode for the chroma block based on an intraprediction mode for a luma block corresponding to the chroma block;modifying the updated intra prediction mode to a wide angle intraprediction mode based on a width of the chroma block not being equal toa height of the chroma block; determining an LFNST set comprising LFNSTmatrices based on a modified intra prediction mode by the wide angleintra prediction mode mapping process; and performing a matrix operationbased on an LFNST matrix derived from the LFNST index and the LFNST set;wherein the updated intra prediction mode is derived as an intraprediction mode corresponding to a specific position in the luma block,wherein the specific position is set to ((xTbY+(nTbW*SubWidthC)/2),(yTbY+(nTbH*SubHeightC)/2)), wherein xTbY and yTbY denote top-leftcoordinates of the luma block, wherein nTbW and nTbH denote the widthand the height of the chroma block, and wherein SubWidthC and SubHeightCdenote variables corresponding to a color format.
 2. The image decodingmethod of claim 1, wherein when the color format is 4:2:0, SubWidthC andSubHeightC are 2, and wherein when the color format is 4:2:2, SubWidthCis 2 and SubHeightC is
 1. 3. The image decoding method of claim 1,wherein when the intra prediction mode corresponding to the specificposition is a palette mode or an IBC mode, the intra prediction mode ofthe chroma block is updated to an intra DC mode.
 4. The image decodingmethod of claim 1, wherein when the intra prediction mode correspondingto the specific position is an MIP mode, the intra prediction mode ofthe chroma block is updated to an intra planar mode.
 5. The imagedecoding method of claim 1, wherein when the width of the chroma blockis greater than the height, the updated intra mode is 2 or more and theupdated intra mode is less than variable (whRatio >1)?(8+2*whRatio):8[where whRatio is Abs(Log 2(nW/nH))], the updated intra mode is modifiedto “updated intra mode+65”.
 6. The image decoding method of claim 1,wherein when the height of the chroma block is greater than the width,the updated intra mode is 66 or less, and the updated intra mode isgreater than variable (whRatio >1)?(60−2*whRatio):60 [where whRatio isAbs(Log 2(nW/nH))], the updated intra mode is modified to “updated intramode−67”.
 7. An image encoding method performed by an encodingapparatus, the method comprising: deriving an intra prediction mode fora chroma block as a cross-component linear model (CCLM) mode; derivingprediction samples for the chroma block based on the CCLM mode; derivingresidual samples for the chroma block based on the prediction samples;and performing an LFNST to derive transform coefficients; wherein theperforming of the LFNST comprising: updating the intra prediction modefor the chroma block based on an intra prediction mode for a luma blockcorresponding to the chroma block; modifying the updated intraprediction mode to a wide angle intra prediction mode based on a widthof the chroma block not being equal to a height of the chroma block;determining an LFNST set comprising LFNST matrices based on a modifiedintra prediction mode by the wide angle intra prediction mode mappingprocess; and performing a matrix operation based on one LFNST matrix,wherein the updated intra prediction mode is derived as an intraprediction mode corresponding to a specific position in the luma block,wherein the specific position is set to ((xTbY+(nTbW*SubWidthC)/2),(yTbY+(nTbH*SubHeightC)/2)), wherein xTbY and yTbY denote top-leftcoordinates of the luma block, wherein nTbW and nTbH denote the widthand the height of the chroma block, and wherein SubWidthC and SubHeightCdenote variables corresponding to a color format.
 8. The image encodingmethod of claim 7, wherein when the color format is 4:2:0, SubWidthC andSubHeightC are 2, and wherein when the color format is 4:2:2, SubWidthCis 2 and SubHeightC is
 1. 9. The image encoding method of claim 7,wherein when the intra prediction mode corresponding to the specificposition is a palette mode or an IBC mode, the intra prediction mode ofthe chroma block is updated to an intra DC mode.
 10. The image encodingmethod of claim 7, wherein when the intra prediction mode correspondingto the specific position is an MIP mode, the intra prediction mode ofthe chroma block is updated to an intra planar mode.
 11. Anon-transitory computer-readable digital storage medium that stores abitstream generated by the image encoding method of claim
 7. 12. Atransmitting method of data for an image, the method comprising:obtaining a bitstream for the image, wherein the bitstream is generatedbased on deriving an intra prediction mode for a chroma block as across-component linear model (CCLM) mode; deriving prediction samplesfor the chroma block based on the CCLM mode; deriving residual samplesfor the chroma block based on the prediction samples; performing anLFNST to derive transform coefficients; and encoding image informationrelated to the transform coefficients; and transmitting the datacomprising the bitstream, wherein the performing of the LFNSTcomprising: updating the intra prediction mode for the chroma blockbased on an intra prediction mode for a luma block corresponding to thechroma block; modifying the updated intra prediction mode to a wideangle intra prediction mode based on a width of the chroma block notbeing equal to a height of the chroma block; determining an LFNST setcomprising LFNST matrices based on a modified intra prediction mode bythe wide angle intra prediction mode mapping process; and performing amatrix operation based on one LFNST matrix, wherein the updated intraprediction mode is derived as an intra prediction mode corresponding toa specific position in the luma block, wherein the specific position isset to ((xTbY+(nTbW*SubWidthC)/2), (yTbY+(nTbH*SubHeightC)/2)), whereinxTbY and yTbY denote top-left coordinates of the luma block, whereinnTbW and nTbH denote the width and the height of the chroma block, andwherein SubWidthC and SubHeightC denote variables corresponding to acolor format.